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-rw-r--r--synapse/api/auth.py41
-rw-r--r--synapse/api/errors.py4
-rw-r--r--synapse/api/filtering.py2
-rw-r--r--synapse/api/ratelimiting.py4
-rw-r--r--synapse/api/room_versions.py4
-rw-r--r--synapse/app/generic_worker.py2
-rw-r--r--synapse/appservice/api.py4
-rw-r--r--synapse/config/appservice.py4
-rw-r--r--synapse/config/cache.py4
-rw-r--r--synapse/config/emailconfig.py4
-rw-r--r--synapse/config/experimental.py6
-rw-r--r--synapse/config/federation.py2
-rw-r--r--synapse/config/oidc.py2
-rw-r--r--synapse/config/password_auth_providers.py2
-rw-r--r--synapse/config/repository.py4
-rw-r--r--synapse/config/server.py16
-rw-r--r--synapse/config/spam_checker.py2
-rw-r--r--synapse/config/sso.py2
-rw-r--r--synapse/config/stats.py9
-rw-r--r--synapse/config/tls.py6
-rw-r--r--synapse/crypto/keyring.py20
-rw-r--r--synapse/event_auth.py11
-rw-r--r--synapse/events/__init__.py26
-rw-r--r--synapse/events/builder.py16
-rw-r--r--synapse/events/spamcheck.py4
-rw-r--r--synapse/federation/federation_client.py10
-rw-r--r--synapse/federation/federation_server.py34
-rw-r--r--synapse/federation/send_queue.py26
-rw-r--r--synapse/federation/sender/__init__.py110
-rw-r--r--synapse/federation/sender/per_destination_queue.py34
-rw-r--r--synapse/federation/transport/client.py8
-rw-r--r--synapse/federation/transport/server.py120
-rw-r--r--synapse/groups/groups_server.py12
-rw-r--r--synapse/handlers/directory.py5
-rw-r--r--synapse/handlers/federation.py25
-rw-r--r--synapse/handlers/message.py18
-rw-r--r--synapse/handlers/receipts.py15
-rw-r--r--synapse/handlers/room_list.py26
-rw-r--r--synapse/handlers/space_summary.py68
-rw-r--r--synapse/handlers/stats.py27
-rw-r--r--synapse/handlers/typing.py14
-rw-r--r--synapse/http/__init__.py2
-rw-r--r--synapse/http/client.py18
-rw-r--r--synapse/http/matrixfederationclient.py40
-rw-r--r--synapse/http/proxyagent.py12
-rw-r--r--synapse/http/server.py8
-rw-r--r--synapse/http/servlet.py2
-rw-r--r--synapse/http/site.py14
-rw-r--r--synapse/logging/_remote.py14
-rw-r--r--synapse/logging/_structured.py2
-rw-r--r--synapse/logging/context.py16
-rw-r--r--synapse/logging/opentracing.py10
-rw-r--r--synapse/metrics/__init__.py6
-rw-r--r--synapse/metrics/_exposition.py2
-rw-r--r--synapse/metrics/background_process_metrics.py4
-rw-r--r--synapse/module_api/__init__.py2
-rw-r--r--synapse/notifier.py18
-rw-r--r--synapse/push/bulk_push_rule_evaluator.py4
-rw-r--r--synapse/push/clientformat.py4
-rw-r--r--synapse/push/emailpusher.py6
-rw-r--r--synapse/push/httppusher.py2
-rw-r--r--synapse/push/mailer.py12
-rw-r--r--synapse/push/presentable_names.py2
-rw-r--r--synapse/push/push_rule_evaluator.py4
-rw-r--r--synapse/push/pusher.py6
-rw-r--r--synapse/push/pusherpool.py2
-rw-r--r--synapse/python_dependencies.py4
-rw-r--r--synapse/replication/http/_base.py10
-rw-r--r--synapse/replication/slave/storage/_base.py6
-rw-r--r--synapse/replication/slave/storage/client_ips.py4
-rw-r--r--synapse/replication/tcp/client.py10
-rw-r--r--synapse/replication/tcp/commands.py6
-rw-r--r--synapse/replication/tcp/handler.py16
-rw-r--r--synapse/replication/tcp/protocol.py14
-rw-r--r--synapse/replication/tcp/redis.py8
-rw-r--r--synapse/replication/tcp/streams/_base.py14
-rw-r--r--synapse/replication/tcp/streams/events.py28
-rw-r--r--synapse/replication/tcp/streams/federation.py6
-rw-r--r--synapse/rest/admin/rooms.py9
-rw-r--r--synapse/rest/client/v1/room.py157
-rw-r--r--synapse/server.py6
-rw-r--r--synapse/server_notices/consent_server_notices.py2
-rw-r--r--synapse/server_notices/resource_limits_server_notices.py2
-rw-r--r--synapse/server_notices/server_notices_sender.py6
-rw-r--r--synapse/state/__init__.py20
-rw-r--r--synapse/state/v1.py2
-rw-r--r--synapse/state/v2.py18
-rw-r--r--synapse/storage/databases/main/event_federation.py4
-rw-r--r--synapse/storage/databases/main/events.py4
-rw-r--r--synapse/storage/databases/main/metrics.py4
-rw-r--r--synapse/storage/databases/main/purge_events.py2
-rw-r--r--synapse/storage/databases/main/room.py104
-rw-r--r--synapse/storage/databases/main/roommember.py13
-rw-r--r--synapse/storage/databases/main/stats.py299
-rw-r--r--synapse/storage/schema/__init__.py6
-rw-r--r--synapse/storage/schema/main/delta/61/01change_appservices_txns.sql.postgres23
-rw-r--r--synapse/storage/schema/main/delta/61/02drop_redundant_room_depth_index.sql18
-rw-r--r--synapse/storage/schema/main/delta/61/03recreate_min_depth.py70
-rw-r--r--synapse/streams/events.py4
-rw-r--r--synapse/types.py10
-rw-r--r--synapse/visibility.py2
101 files changed, 1088 insertions, 788 deletions
diff --git a/synapse/api/auth.py b/synapse/api/auth.py
index 307f5f9a94..8916e6fa2f 100644
--- a/synapse/api/auth.py
+++ b/synapse/api/auth.py
@@ -63,9 +63,9 @@ class Auth:
         self.store = hs.get_datastore()
         self.state = hs.get_state_handler()
 
-        self.token_cache = LruCache(
+        self.token_cache: LruCache[str, Tuple[str, bool]] = LruCache(
             10000, "token_cache"
-        )  # type: LruCache[str, Tuple[str, bool]]
+        )
 
         self._auth_blocking = AuthBlocking(self.hs)
 
@@ -240,6 +240,37 @@ class Auth:
         except KeyError:
             raise MissingClientTokenError()
 
+    async def validate_appservice_can_control_user_id(
+        self, app_service: ApplicationService, user_id: str
+    ):
+        """Validates that the app service is allowed to control
+        the given user.
+
+        Args:
+            app_service: The app service that controls the user
+            user_id: The author MXID that the app service is controlling
+
+        Raises:
+            AuthError: If the application service is not allowed to control the user
+                (user namespace regex does not match, wrong homeserver, etc)
+                or if the user has not been registered yet.
+        """
+
+        # It's ok if the app service is trying to use the sender from their registration
+        if app_service.sender == user_id:
+            pass
+        # Check to make sure the app service is allowed to control the user
+        elif not app_service.is_interested_in_user(user_id):
+            raise AuthError(
+                403,
+                "Application service cannot masquerade as this user (%s)." % user_id,
+            )
+        # Check to make sure the user is already registered on the homeserver
+        elif not (await self.store.get_user_by_id(user_id)):
+            raise AuthError(
+                403, "Application service has not registered this user (%s)" % user_id
+            )
+
     async def _get_appservice_user_id(
         self, request: Request
     ) -> Tuple[Optional[str], Optional[ApplicationService]]:
@@ -261,13 +292,11 @@ class Auth:
             return app_service.sender, app_service
 
         user_id = request.args[b"user_id"][0].decode("utf8")
+        await self.validate_appservice_can_control_user_id(app_service, user_id)
+
         if app_service.sender == user_id:
             return app_service.sender, app_service
 
-        if not app_service.is_interested_in_user(user_id):
-            raise AuthError(403, "Application service cannot masquerade as this user.")
-        if not (await self.store.get_user_by_id(user_id)):
-            raise AuthError(403, "Application service has not registered this user")
         return user_id, app_service
 
     async def get_user_by_access_token(
diff --git a/synapse/api/errors.py b/synapse/api/errors.py
index 4cb8bbaf70..054ab14ab6 100644
--- a/synapse/api/errors.py
+++ b/synapse/api/errors.py
@@ -118,7 +118,7 @@ class RedirectException(CodeMessageException):
         super().__init__(code=http_code, msg=msg)
         self.location = location
 
-        self.cookies = []  # type: List[bytes]
+        self.cookies: List[bytes] = []
 
 
 class SynapseError(CodeMessageException):
@@ -160,7 +160,7 @@ class ProxiedRequestError(SynapseError):
     ):
         super().__init__(code, msg, errcode)
         if additional_fields is None:
-            self._additional_fields = {}  # type: Dict
+            self._additional_fields: Dict = {}
         else:
             self._additional_fields = dict(additional_fields)
 
diff --git a/synapse/api/filtering.py b/synapse/api/filtering.py
index ce49a0ad58..ad1ff6a9df 100644
--- a/synapse/api/filtering.py
+++ b/synapse/api/filtering.py
@@ -289,7 +289,7 @@ class Filter:
             room_id = None
             ev_type = "m.presence"
             contains_url = False
-            labels = []  # type: List[str]
+            labels: List[str] = []
         else:
             sender = event.get("sender", None)
             if not sender:
diff --git a/synapse/api/ratelimiting.py b/synapse/api/ratelimiting.py
index b9a10283f4..3e3d09bbd2 100644
--- a/synapse/api/ratelimiting.py
+++ b/synapse/api/ratelimiting.py
@@ -46,9 +46,7 @@ class Ratelimiter:
         #   * How many times an action has occurred since a point in time
         #   * The point in time
         #   * The rate_hz of this particular entry. This can vary per request
-        self.actions = (
-            OrderedDict()
-        )  # type: OrderedDict[Hashable, Tuple[float, int, float]]
+        self.actions: OrderedDict[Hashable, Tuple[float, int, float]] = OrderedDict()
 
     async def can_do_action(
         self,
diff --git a/synapse/api/room_versions.py b/synapse/api/room_versions.py
index f6c1c97b40..a20abc5a65 100644
--- a/synapse/api/room_versions.py
+++ b/synapse/api/room_versions.py
@@ -195,7 +195,7 @@ class RoomVersions:
     )
 
 
-KNOWN_ROOM_VERSIONS = {
+KNOWN_ROOM_VERSIONS: Dict[str, RoomVersion] = {
     v.identifier: v
     for v in (
         RoomVersions.V1,
@@ -209,4 +209,4 @@ KNOWN_ROOM_VERSIONS = {
         RoomVersions.V7,
     )
     # Note that we do not include MSC2043 here unless it is enabled in the config.
-}  # type: Dict[str, RoomVersion]
+}
diff --git a/synapse/app/generic_worker.py b/synapse/app/generic_worker.py
index 5b041fcaad..b43d858f59 100644
--- a/synapse/app/generic_worker.py
+++ b/synapse/app/generic_worker.py
@@ -270,7 +270,7 @@ class GenericWorkerServer(HomeServer):
             site_tag = port
 
         # We always include a health resource.
-        resources = {"/health": HealthResource()}  # type: Dict[str, IResource]
+        resources: Dict[str, IResource] = {"/health": HealthResource()}
 
         for res in listener_config.http_options.resources:
             for name in res.names:
diff --git a/synapse/appservice/api.py b/synapse/appservice/api.py
index 61152b2c46..935f24263c 100644
--- a/synapse/appservice/api.py
+++ b/synapse/appservice/api.py
@@ -88,9 +88,9 @@ class ApplicationServiceApi(SimpleHttpClient):
         super().__init__(hs)
         self.clock = hs.get_clock()
 
-        self.protocol_meta_cache = ResponseCache(
+        self.protocol_meta_cache: ResponseCache[Tuple[str, str]] = ResponseCache(
             hs.get_clock(), "as_protocol_meta", timeout_ms=HOUR_IN_MS
-        )  # type: ResponseCache[Tuple[str, str]]
+        )
 
     async def query_user(self, service, user_id):
         if service.url is None:
diff --git a/synapse/config/appservice.py b/synapse/config/appservice.py
index 746fc3cc02..a39d457c56 100644
--- a/synapse/config/appservice.py
+++ b/synapse/config/appservice.py
@@ -57,8 +57,8 @@ def load_appservices(hostname, config_files):
         return []
 
     # Dicts of value -> filename
-    seen_as_tokens = {}  # type: Dict[str, str]
-    seen_ids = {}  # type: Dict[str, str]
+    seen_as_tokens: Dict[str, str] = {}
+    seen_ids: Dict[str, str] = {}
 
     appservices = []
 
diff --git a/synapse/config/cache.py b/synapse/config/cache.py
index 7789b40323..8d5f38b5d9 100644
--- a/synapse/config/cache.py
+++ b/synapse/config/cache.py
@@ -25,7 +25,7 @@ from ._base import Config, ConfigError
 _CACHE_PREFIX = "SYNAPSE_CACHE_FACTOR"
 
 # Map from canonicalised cache name to cache.
-_CACHES = {}  # type: Dict[str, Callable[[float], None]]
+_CACHES: Dict[str, Callable[[float], None]] = {}
 
 # a lock on the contents of _CACHES
 _CACHES_LOCK = threading.Lock()
@@ -157,7 +157,7 @@ class CacheConfig(Config):
         self.event_cache_size = self.parse_size(
             config.get("event_cache_size", _DEFAULT_EVENT_CACHE_SIZE)
         )
-        self.cache_factors = {}  # type: Dict[str, float]
+        self.cache_factors: Dict[str, float] = {}
 
         cache_config = config.get("caches") or {}
         self.global_factor = cache_config.get(
diff --git a/synapse/config/emailconfig.py b/synapse/config/emailconfig.py
index 5564d7d097..bcecbfec03 100644
--- a/synapse/config/emailconfig.py
+++ b/synapse/config/emailconfig.py
@@ -134,9 +134,9 @@ class EmailConfig(Config):
 
                 # trusted_third_party_id_servers does not contain a scheme whereas
                 # account_threepid_delegate_email is expected to. Presume https
-                self.account_threepid_delegate_email = (
+                self.account_threepid_delegate_email: Optional[str] = (
                     "https://" + first_trusted_identity_server
-                )  # type: Optional[str]
+                )
                 self.using_identity_server_from_trusted_list = True
             else:
                 raise ConfigError(
diff --git a/synapse/config/experimental.py b/synapse/config/experimental.py
index 7fb1f7021f..e25ccba9ac 100644
--- a/synapse/config/experimental.py
+++ b/synapse/config/experimental.py
@@ -25,10 +25,10 @@ class ExperimentalConfig(Config):
         experimental = config.get("experimental_features") or {}
 
         # MSC2858 (multiple SSO identity providers)
-        self.msc2858_enabled = experimental.get("msc2858_enabled", False)  # type: bool
+        self.msc2858_enabled: bool = experimental.get("msc2858_enabled", False)
 
         # MSC3026 (busy presence state)
-        self.msc3026_enabled = experimental.get("msc3026_enabled", False)  # type: bool
+        self.msc3026_enabled: bool = experimental.get("msc3026_enabled", False)
 
         # MSC2716 (backfill existing history)
-        self.msc2716_enabled = experimental.get("msc2716_enabled", False)  # type: bool
+        self.msc2716_enabled: bool = experimental.get("msc2716_enabled", False)
diff --git a/synapse/config/federation.py b/synapse/config/federation.py
index cdd7a1ef05..7d64993e22 100644
--- a/synapse/config/federation.py
+++ b/synapse/config/federation.py
@@ -22,7 +22,7 @@ class FederationConfig(Config):
 
     def read_config(self, config, **kwargs):
         # FIXME: federation_domain_whitelist needs sytests
-        self.federation_domain_whitelist = None  # type: Optional[dict]
+        self.federation_domain_whitelist: Optional[dict] = None
         federation_domain_whitelist = config.get("federation_domain_whitelist", None)
 
         if federation_domain_whitelist is not None:
diff --git a/synapse/config/oidc.py b/synapse/config/oidc.py
index 942e2672a9..ba89d11cf0 100644
--- a/synapse/config/oidc.py
+++ b/synapse/config/oidc.py
@@ -460,7 +460,7 @@ def _parse_oidc_config_dict(
             ) from e
 
     client_secret_jwt_key_config = oidc_config.get("client_secret_jwt_key")
-    client_secret_jwt_key = None  # type: Optional[OidcProviderClientSecretJwtKey]
+    client_secret_jwt_key: Optional[OidcProviderClientSecretJwtKey] = None
     if client_secret_jwt_key_config is not None:
         keyfile = client_secret_jwt_key_config.get("key_file")
         if keyfile:
diff --git a/synapse/config/password_auth_providers.py b/synapse/config/password_auth_providers.py
index fd90b79772..0f5b2b3977 100644
--- a/synapse/config/password_auth_providers.py
+++ b/synapse/config/password_auth_providers.py
@@ -25,7 +25,7 @@ class PasswordAuthProviderConfig(Config):
     section = "authproviders"
 
     def read_config(self, config, **kwargs):
-        self.password_providers = []  # type: List[Any]
+        self.password_providers: List[Any] = []
         providers = []
 
         # We want to be backwards compatible with the old `ldap_config`
diff --git a/synapse/config/repository.py b/synapse/config/repository.py
index a7a82742ac..0dfb3a227a 100644
--- a/synapse/config/repository.py
+++ b/synapse/config/repository.py
@@ -62,7 +62,7 @@ def parse_thumbnail_requirements(thumbnail_sizes):
         Dictionary mapping from media type string to list of
         ThumbnailRequirement tuples.
     """
-    requirements = {}  # type: Dict[str, List]
+    requirements: Dict[str, List] = {}
     for size in thumbnail_sizes:
         width = size["width"]
         height = size["height"]
@@ -141,7 +141,7 @@ class ContentRepositoryConfig(Config):
         #
         # We don't create the storage providers here as not all workers need
         # them to be started.
-        self.media_storage_providers = []  # type: List[tuple]
+        self.media_storage_providers: List[tuple] = []
 
         for i, provider_config in enumerate(storage_providers):
             # We special case the module "file_system" so as not to need to
diff --git a/synapse/config/server.py b/synapse/config/server.py
index 6bff715230..b9e0c0b300 100644
--- a/synapse/config/server.py
+++ b/synapse/config/server.py
@@ -505,7 +505,7 @@ class ServerConfig(Config):
                 " greater than 'allowed_lifetime_max'"
             )
 
-        self.retention_purge_jobs = []  # type: List[Dict[str, Optional[int]]]
+        self.retention_purge_jobs: List[Dict[str, Optional[int]]] = []
         for purge_job_config in retention_config.get("purge_jobs", []):
             interval_config = purge_job_config.get("interval")
 
@@ -688,23 +688,21 @@ class ServerConfig(Config):
         # not included in the sample configuration file on purpose as it's a temporary
         # hack, so that some users can trial the new defaults without impacting every
         # user on the homeserver.
-        users_new_default_push_rules = (
+        users_new_default_push_rules: list = (
             config.get("users_new_default_push_rules") or []
-        )  # type: list
+        )
         if not isinstance(users_new_default_push_rules, list):
             raise ConfigError("'users_new_default_push_rules' must be a list")
 
         # Turn the list into a set to improve lookup speed.
-        self.users_new_default_push_rules = set(
-            users_new_default_push_rules
-        )  # type: set
+        self.users_new_default_push_rules: set = set(users_new_default_push_rules)
 
         # Whitelist of domain names that given next_link parameters must have
-        next_link_domain_whitelist = config.get(
+        next_link_domain_whitelist: Optional[List[str]] = config.get(
             "next_link_domain_whitelist"
-        )  # type: Optional[List[str]]
+        )
 
-        self.next_link_domain_whitelist = None  # type: Optional[Set[str]]
+        self.next_link_domain_whitelist: Optional[Set[str]] = None
         if next_link_domain_whitelist is not None:
             if not isinstance(next_link_domain_whitelist, list):
                 raise ConfigError("'next_link_domain_whitelist' must be a list")
diff --git a/synapse/config/spam_checker.py b/synapse/config/spam_checker.py
index cb7716c837..a233a9ce03 100644
--- a/synapse/config/spam_checker.py
+++ b/synapse/config/spam_checker.py
@@ -34,7 +34,7 @@ class SpamCheckerConfig(Config):
     section = "spamchecker"
 
     def read_config(self, config, **kwargs):
-        self.spam_checkers = []  # type: List[Tuple[Any, Dict]]
+        self.spam_checkers: List[Tuple[Any, Dict]] = []
 
         spam_checkers = config.get("spam_checker") or []
         if isinstance(spam_checkers, dict):
diff --git a/synapse/config/sso.py b/synapse/config/sso.py
index e4346e02aa..d0f04cf8e6 100644
--- a/synapse/config/sso.py
+++ b/synapse/config/sso.py
@@ -39,7 +39,7 @@ class SSOConfig(Config):
     section = "sso"
 
     def read_config(self, config, **kwargs):
-        sso_config = config.get("sso") or {}  # type: Dict[str, Any]
+        sso_config: Dict[str, Any] = config.get("sso") or {}
 
         # The sso-specific template_dir
         self.sso_template_dir = sso_config.get("template_dir")
diff --git a/synapse/config/stats.py b/synapse/config/stats.py
index 78f61fe9da..6f253e00c0 100644
--- a/synapse/config/stats.py
+++ b/synapse/config/stats.py
@@ -38,13 +38,9 @@ class StatsConfig(Config):
 
     def read_config(self, config, **kwargs):
         self.stats_enabled = True
-        self.stats_bucket_size = 86400 * 1000
         stats_config = config.get("stats", None)
         if stats_config:
             self.stats_enabled = stats_config.get("enabled", self.stats_enabled)
-            self.stats_bucket_size = self.parse_duration(
-                stats_config.get("bucket_size", "1d")
-            )
         if not self.stats_enabled:
             logger.warning(ROOM_STATS_DISABLED_WARN)
 
@@ -59,9 +55,4 @@ class StatsConfig(Config):
           # correctly.
           #
           #enabled: false
-
-          # The size of each timeslice in the room_stats_historical and
-          # user_stats_historical tables, as a time period. Defaults to "1d".
-          #
-          #bucket_size: 1h
         """
diff --git a/synapse/config/tls.py b/synapse/config/tls.py
index 9a16a8fbae..fed05ac7be 100644
--- a/synapse/config/tls.py
+++ b/synapse/config/tls.py
@@ -80,7 +80,7 @@ class TlsConfig(Config):
             fed_whitelist_entries = []
 
         # Support globs (*) in whitelist values
-        self.federation_certificate_verification_whitelist = []  # type: List[Pattern]
+        self.federation_certificate_verification_whitelist: List[Pattern] = []
         for entry in fed_whitelist_entries:
             try:
                 entry_regex = glob_to_regex(entry.encode("ascii").decode("ascii"))
@@ -132,8 +132,8 @@ class TlsConfig(Config):
             "use_insecure_ssl_client_just_for_testing_do_not_use"
         )
 
-        self.tls_certificate = None  # type: Optional[crypto.X509]
-        self.tls_private_key = None  # type: Optional[crypto.PKey]
+        self.tls_certificate: Optional[crypto.X509] = None
+        self.tls_private_key: Optional[crypto.PKey] = None
 
     def is_disk_cert_valid(self, allow_self_signed=True):
         """
diff --git a/synapse/crypto/keyring.py b/synapse/crypto/keyring.py
index e5a4685ed4..9e9b1c1c86 100644
--- a/synapse/crypto/keyring.py
+++ b/synapse/crypto/keyring.py
@@ -170,11 +170,13 @@ class Keyring:
             )
         self._key_fetchers = key_fetchers
 
-        self._server_queue = BatchingQueue(
+        self._server_queue: BatchingQueue[
+            _FetchKeyRequest, Dict[str, Dict[str, FetchKeyResult]]
+        ] = BatchingQueue(
             "keyring_server",
             clock=hs.get_clock(),
             process_batch_callback=self._inner_fetch_key_requests,
-        )  # type: BatchingQueue[_FetchKeyRequest, Dict[str, Dict[str, FetchKeyResult]]]
+        )
 
     async def verify_json_for_server(
         self,
@@ -330,7 +332,7 @@ class Keyring:
         # First we need to deduplicate requests for the same key. We do this by
         # taking the *maximum* requested `minimum_valid_until_ts` for each pair
         # of server name/key ID.
-        server_to_key_to_ts = {}  # type: Dict[str, Dict[str, int]]
+        server_to_key_to_ts: Dict[str, Dict[str, int]] = {}
         for request in requests:
             by_server = server_to_key_to_ts.setdefault(request.server_name, {})
             for key_id in request.key_ids:
@@ -355,7 +357,7 @@ class Keyring:
 
         # We now convert the returned list of results into a map from server
         # name to key ID to FetchKeyResult, to return.
-        to_return = {}  # type: Dict[str, Dict[str, FetchKeyResult]]
+        to_return: Dict[str, Dict[str, FetchKeyResult]] = {}
         for (request, results) in zip(deduped_requests, results_per_request):
             to_return_by_server = to_return.setdefault(request.server_name, {})
             for key_id, key_result in results.items():
@@ -455,7 +457,7 @@ class StoreKeyFetcher(KeyFetcher):
         )
 
         res = await self.store.get_server_verify_keys(key_ids_to_fetch)
-        keys = {}  # type: Dict[str, Dict[str, FetchKeyResult]]
+        keys: Dict[str, Dict[str, FetchKeyResult]] = {}
         for (server_name, key_id), key in res.items():
             keys.setdefault(server_name, {})[key_id] = key
         return keys
@@ -603,7 +605,7 @@ class PerspectivesKeyFetcher(BaseV2KeyFetcher):
             ).addErrback(unwrapFirstError)
         )
 
-        union_of_keys = {}  # type: Dict[str, Dict[str, FetchKeyResult]]
+        union_of_keys: Dict[str, Dict[str, FetchKeyResult]] = {}
         for result in results:
             for server_name, keys in result.items():
                 union_of_keys.setdefault(server_name, {}).update(keys)
@@ -656,8 +658,8 @@ class PerspectivesKeyFetcher(BaseV2KeyFetcher):
         except HttpResponseException as e:
             raise KeyLookupError("Remote server returned an error: %s" % (e,))
 
-        keys = {}  # type: Dict[str, Dict[str, FetchKeyResult]]
-        added_keys = []  # type: List[Tuple[str, str, FetchKeyResult]]
+        keys: Dict[str, Dict[str, FetchKeyResult]] = {}
+        added_keys: List[Tuple[str, str, FetchKeyResult]] = []
 
         time_now_ms = self.clock.time_msec()
 
@@ -805,7 +807,7 @@ class ServerKeyFetcher(BaseV2KeyFetcher):
         Raises:
             KeyLookupError if there was a problem making the lookup
         """
-        keys = {}  # type: Dict[str, FetchKeyResult]
+        keys: Dict[str, FetchKeyResult] = {}
 
         for requested_key_id in key_ids:
             # we may have found this key as a side-effect of asking for another.
diff --git a/synapse/event_auth.py b/synapse/event_auth.py
index 89bcf81515..137dff2513 100644
--- a/synapse/event_auth.py
+++ b/synapse/event_auth.py
@@ -48,6 +48,9 @@ def check(
         room_version_obj: the version of the room
         event: the event being checked.
         auth_events: the existing room state.
+        do_sig_check: True if it should be verified that the sending server
+            signed the event.
+        do_size_check: True if the size of the event fields should be verified.
 
     Raises:
         AuthError if the checks fail
@@ -528,7 +531,7 @@ def _check_power_levels(
     user_level = get_user_power_level(event.user_id, auth_events)
 
     # Check other levels:
-    levels_to_check = [
+    levels_to_check: List[Tuple[str, Optional[str]]] = [
         ("users_default", None),
         ("events_default", None),
         ("state_default", None),
@@ -536,7 +539,7 @@ def _check_power_levels(
         ("redact", None),
         ("kick", None),
         ("invite", None),
-    ]  # type: List[Tuple[str, Optional[str]]]
+    ]
 
     old_list = current_state.content.get("users", {})
     for user in set(list(old_list) + list(user_list)):
@@ -566,12 +569,12 @@ def _check_power_levels(
             new_loc = new_loc.get(dir, {})
 
         if level_to_check in old_loc:
-            old_level = int(old_loc[level_to_check])  # type: Optional[int]
+            old_level: Optional[int] = int(old_loc[level_to_check])
         else:
             old_level = None
 
         if level_to_check in new_loc:
-            new_level = int(new_loc[level_to_check])  # type: Optional[int]
+            new_level: Optional[int] = int(new_loc[level_to_check])
         else:
             new_level = None
 
diff --git a/synapse/events/__init__.py b/synapse/events/__init__.py
index 6286ad999a..65dc7a4ed0 100644
--- a/synapse/events/__init__.py
+++ b/synapse/events/__init__.py
@@ -105,28 +105,28 @@ class _EventInternalMetadata:
         self._dict = dict(internal_metadata_dict)
 
         # the stream ordering of this event. None, until it has been persisted.
-        self.stream_ordering = None  # type: Optional[int]
+        self.stream_ordering: Optional[int] = None
 
         # whether this event is an outlier (ie, whether we have the state at that point
         # in the DAG)
         self.outlier = False
 
-    out_of_band_membership = DictProperty("out_of_band_membership")  # type: bool
-    send_on_behalf_of = DictProperty("send_on_behalf_of")  # type: str
-    recheck_redaction = DictProperty("recheck_redaction")  # type: bool
-    soft_failed = DictProperty("soft_failed")  # type: bool
-    proactively_send = DictProperty("proactively_send")  # type: bool
-    redacted = DictProperty("redacted")  # type: bool
-    txn_id = DictProperty("txn_id")  # type: str
-    token_id = DictProperty("token_id")  # type: int
-    historical = DictProperty("historical")  # type: bool
+    out_of_band_membership: bool = DictProperty("out_of_band_membership")
+    send_on_behalf_of: str = DictProperty("send_on_behalf_of")
+    recheck_redaction: bool = DictProperty("recheck_redaction")
+    soft_failed: bool = DictProperty("soft_failed")
+    proactively_send: bool = DictProperty("proactively_send")
+    redacted: bool = DictProperty("redacted")
+    txn_id: str = DictProperty("txn_id")
+    token_id: int = DictProperty("token_id")
+    historical: bool = DictProperty("historical")
 
     # XXX: These are set by StreamWorkerStore._set_before_and_after.
     # I'm pretty sure that these are never persisted to the database, so shouldn't
     # be here
-    before = DictProperty("before")  # type: RoomStreamToken
-    after = DictProperty("after")  # type: RoomStreamToken
-    order = DictProperty("order")  # type: Tuple[int, int]
+    before: RoomStreamToken = DictProperty("before")
+    after: RoomStreamToken = DictProperty("after")
+    order: Tuple[int, int] = DictProperty("order")
 
     def get_dict(self) -> JsonDict:
         return dict(self._dict)
diff --git a/synapse/events/builder.py b/synapse/events/builder.py
index 26e3950859..87e2bb123b 100644
--- a/synapse/events/builder.py
+++ b/synapse/events/builder.py
@@ -132,12 +132,12 @@ class EventBuilder:
         format_version = self.room_version.event_format
         if format_version == EventFormatVersions.V1:
             # The types of auth/prev events changes between event versions.
-            auth_events = await self._store.add_event_hashes(
-                auth_event_ids
-            )  # type: Union[List[str], List[Tuple[str, Dict[str, str]]]]
-            prev_events = await self._store.add_event_hashes(
-                prev_event_ids
-            )  # type: Union[List[str], List[Tuple[str, Dict[str, str]]]]
+            auth_events: Union[
+                List[str], List[Tuple[str, Dict[str, str]]]
+            ] = await self._store.add_event_hashes(auth_event_ids)
+            prev_events: Union[
+                List[str], List[Tuple[str, Dict[str, str]]]
+            ] = await self._store.add_event_hashes(prev_event_ids)
         else:
             auth_events = auth_event_ids
             prev_events = prev_event_ids
@@ -156,7 +156,7 @@ class EventBuilder:
         # the db)
         depth = min(depth, MAX_DEPTH)
 
-        event_dict = {
+        event_dict: Dict[str, Any] = {
             "auth_events": auth_events,
             "prev_events": prev_events,
             "type": self.type,
@@ -166,7 +166,7 @@ class EventBuilder:
             "unsigned": self.unsigned,
             "depth": depth,
             "prev_state": [],
-        }  # type: Dict[str, Any]
+        }
 
         if self.is_state():
             event_dict["state_key"] = self._state_key
diff --git a/synapse/events/spamcheck.py b/synapse/events/spamcheck.py
index efec16c226..57f1d53fa8 100644
--- a/synapse/events/spamcheck.py
+++ b/synapse/events/spamcheck.py
@@ -76,7 +76,7 @@ def load_legacy_spam_checkers(hs: "synapse.server.HomeServer"):
     """Wrapper that loads spam checkers configured using the old configuration, and
     registers the spam checker hooks they implement.
     """
-    spam_checkers = []  # type: List[Any]
+    spam_checkers: List[Any] = []
     api = hs.get_module_api()
     for module, config in hs.config.spam_checkers:
         # Older spam checkers don't accept the `api` argument, so we
@@ -239,7 +239,7 @@ class SpamChecker:
             will be used as the error message returned to the user.
         """
         for callback in self._check_event_for_spam_callbacks:
-            res = await callback(event)  # type: Union[bool, str]
+            res: Union[bool, str] = await callback(event)
             if res:
                 return res
 
diff --git a/synapse/federation/federation_client.py b/synapse/federation/federation_client.py
index ed09c6af1f..c767d30627 100644
--- a/synapse/federation/federation_client.py
+++ b/synapse/federation/federation_client.py
@@ -86,7 +86,7 @@ class FederationClient(FederationBase):
     def __init__(self, hs: "HomeServer"):
         super().__init__(hs)
 
-        self.pdu_destination_tried = {}  # type: Dict[str, Dict[str, int]]
+        self.pdu_destination_tried: Dict[str, Dict[str, int]] = {}
         self._clock.looping_call(self._clear_tried_cache, 60 * 1000)
         self.state = hs.get_state_handler()
         self.transport_layer = hs.get_federation_transport_client()
@@ -94,13 +94,13 @@ class FederationClient(FederationBase):
         self.hostname = hs.hostname
         self.signing_key = hs.signing_key
 
-        self._get_pdu_cache = ExpiringCache(
+        self._get_pdu_cache: ExpiringCache[str, EventBase] = ExpiringCache(
             cache_name="get_pdu_cache",
             clock=self._clock,
             max_len=1000,
             expiry_ms=120 * 1000,
             reset_expiry_on_get=False,
-        )  # type: ExpiringCache[str, EventBase]
+        )
 
     def _clear_tried_cache(self):
         """Clear pdu_destination_tried cache"""
@@ -293,10 +293,10 @@ class FederationClient(FederationBase):
                     transaction_data,
                 )
 
-                pdu_list = [
+                pdu_list: List[EventBase] = [
                     event_from_pdu_json(p, room_version, outlier=outlier)
                     for p in transaction_data["pdus"]
-                ]  # type: List[EventBase]
+                ]
 
                 if pdu_list and pdu_list[0]:
                     pdu = pdu_list[0]
diff --git a/synapse/federation/federation_server.py b/synapse/federation/federation_server.py
index ac0f2ccfb3..d91f0ff32f 100644
--- a/synapse/federation/federation_server.py
+++ b/synapse/federation/federation_server.py
@@ -122,12 +122,12 @@ class FederationServer(FederationBase):
 
         # origins that we are currently processing a transaction from.
         # a dict from origin to txn id.
-        self._active_transactions = {}  # type: Dict[str, str]
+        self._active_transactions: Dict[str, str] = {}
 
         # We cache results for transaction with the same ID
-        self._transaction_resp_cache = ResponseCache(
+        self._transaction_resp_cache: ResponseCache[Tuple[str, str]] = ResponseCache(
             hs.get_clock(), "fed_txn_handler", timeout_ms=30000
-        )  # type: ResponseCache[Tuple[str, str]]
+        )
 
         self.transaction_actions = TransactionActions(self.store)
 
@@ -135,12 +135,12 @@ class FederationServer(FederationBase):
 
         # We cache responses to state queries, as they take a while and often
         # come in waves.
-        self._state_resp_cache = ResponseCache(
-            hs.get_clock(), "state_resp", timeout_ms=30000
-        )  # type: ResponseCache[Tuple[str, Optional[str]]]
-        self._state_ids_resp_cache = ResponseCache(
+        self._state_resp_cache: ResponseCache[
+            Tuple[str, Optional[str]]
+        ] = ResponseCache(hs.get_clock(), "state_resp", timeout_ms=30000)
+        self._state_ids_resp_cache: ResponseCache[Tuple[str, str]] = ResponseCache(
             hs.get_clock(), "state_ids_resp", timeout_ms=30000
-        )  # type: ResponseCache[Tuple[str, str]]
+        )
 
         self._federation_metrics_domains = (
             hs.config.federation.federation_metrics_domains
@@ -337,7 +337,7 @@ class FederationServer(FederationBase):
 
         origin_host, _ = parse_server_name(origin)
 
-        pdus_by_room = {}  # type: Dict[str, List[EventBase]]
+        pdus_by_room: Dict[str, List[EventBase]] = {}
 
         newest_pdu_ts = 0
 
@@ -516,9 +516,9 @@ class FederationServer(FederationBase):
         self, room_id: str, event_id: Optional[str]
     ) -> Dict[str, list]:
         if event_id:
-            pdus = await self.handler.get_state_for_pdu(
+            pdus: Iterable[EventBase] = await self.handler.get_state_for_pdu(
                 room_id, event_id
-            )  # type: Iterable[EventBase]
+            )
         else:
             pdus = (await self.state.get_current_state(room_id)).values()
 
@@ -791,7 +791,7 @@ class FederationServer(FederationBase):
         log_kv({"message": "Claiming one time keys.", "user, device pairs": query})
         results = await self.store.claim_e2e_one_time_keys(query)
 
-        json_result = {}  # type: Dict[str, Dict[str, dict]]
+        json_result: Dict[str, Dict[str, dict]] = {}
         for user_id, device_keys in results.items():
             for device_id, keys in device_keys.items():
                 for key_id, json_str in keys.items():
@@ -1119,17 +1119,13 @@ class FederationHandlerRegistry:
         self._get_query_client = ReplicationGetQueryRestServlet.make_client(hs)
         self._send_edu = ReplicationFederationSendEduRestServlet.make_client(hs)
 
-        self.edu_handlers = (
-            {}
-        )  # type: Dict[str, Callable[[str, dict], Awaitable[None]]]
-        self.query_handlers = (
-            {}
-        )  # type: Dict[str, Callable[[dict], Awaitable[JsonDict]]]
+        self.edu_handlers: Dict[str, Callable[[str, dict], Awaitable[None]]] = {}
+        self.query_handlers: Dict[str, Callable[[dict], Awaitable[JsonDict]]] = {}
 
         # Map from type to instance names that we should route EDU handling to.
         # We randomly choose one instance from the list to route to for each new
         # EDU received.
-        self._edu_type_to_instance = {}  # type: Dict[str, List[str]]
+        self._edu_type_to_instance: Dict[str, List[str]] = {}
 
     def register_edu_handler(
         self, edu_type: str, handler: Callable[[str, JsonDict], Awaitable[None]]
diff --git a/synapse/federation/send_queue.py b/synapse/federation/send_queue.py
index 65d76ea974..1fbf325fdc 100644
--- a/synapse/federation/send_queue.py
+++ b/synapse/federation/send_queue.py
@@ -71,34 +71,32 @@ class FederationRemoteSendQueue(AbstractFederationSender):
         # We may have multiple federation sender instances, so we need to track
         # their positions separately.
         self._sender_instances = hs.config.worker.federation_shard_config.instances
-        self._sender_positions = {}  # type: Dict[str, int]
+        self._sender_positions: Dict[str, int] = {}
 
         # Pending presence map user_id -> UserPresenceState
-        self.presence_map = {}  # type: Dict[str, UserPresenceState]
+        self.presence_map: Dict[str, UserPresenceState] = {}
 
         # Stores the destinations we need to explicitly send presence to about a
         # given user.
         # Stream position -> (user_id, destinations)
-        self.presence_destinations = (
-            SortedDict()
-        )  # type: SortedDict[int, Tuple[str, Iterable[str]]]
+        self.presence_destinations: SortedDict[
+            int, Tuple[str, Iterable[str]]
+        ] = SortedDict()
 
         # (destination, key) -> EDU
-        self.keyed_edu = {}  # type: Dict[Tuple[str, tuple], Edu]
+        self.keyed_edu: Dict[Tuple[str, tuple], Edu] = {}
 
         # stream position -> (destination, key)
-        self.keyed_edu_changed = (
-            SortedDict()
-        )  # type: SortedDict[int, Tuple[str, tuple]]
+        self.keyed_edu_changed: SortedDict[int, Tuple[str, tuple]] = SortedDict()
 
-        self.edus = SortedDict()  # type: SortedDict[int, Edu]
+        self.edus: SortedDict[int, Edu] = SortedDict()
 
         # stream ID for the next entry into keyed_edu_changed/edus.
         self.pos = 1
 
         # map from stream ID to the time that stream entry was generated, so that we
         # can clear out entries after a while
-        self.pos_time = SortedDict()  # type: SortedDict[int, int]
+        self.pos_time: SortedDict[int, int] = SortedDict()
 
         # EVERYTHING IS SAD. In particular, python only makes new scopes when
         # we make a new function, so we need to make a new function so the inner
@@ -291,7 +289,7 @@ class FederationRemoteSendQueue(AbstractFederationSender):
 
         # list of tuple(int, BaseFederationRow), where the first is the position
         # of the federation stream.
-        rows = []  # type: List[Tuple[int, BaseFederationRow]]
+        rows: List[Tuple[int, BaseFederationRow]] = []
 
         # Fetch presence to send to destinations
         i = self.presence_destinations.bisect_right(from_token)
@@ -445,11 +443,11 @@ class EduRow(BaseFederationRow, namedtuple("EduRow", ("edu",))):  # Edu
         buff.edus.setdefault(self.edu.destination, []).append(self.edu)
 
 
-_rowtypes = (
+_rowtypes: Tuple[Type[BaseFederationRow], ...] = (
     PresenceDestinationsRow,
     KeyedEduRow,
     EduRow,
-)  # type: Tuple[Type[BaseFederationRow], ...]
+)
 
 TypeToRow = {Row.TypeId: Row for Row in _rowtypes}
 
diff --git a/synapse/federation/sender/__init__.py b/synapse/federation/sender/__init__.py
index deb40f4610..d980e0d986 100644
--- a/synapse/federation/sender/__init__.py
+++ b/synapse/federation/sender/__init__.py
@@ -14,9 +14,12 @@
 
 import abc
 import logging
+from collections import OrderedDict
 from typing import TYPE_CHECKING, Dict, Hashable, Iterable, List, Optional, Set, Tuple
 
+import attr
 from prometheus_client import Counter
+from typing_extensions import Literal
 
 from twisted.internet import defer
 
@@ -33,8 +36,12 @@ from synapse.metrics import (
     event_processing_loop_room_count,
     events_processed_counter,
 )
-from synapse.metrics.background_process_metrics import run_as_background_process
+from synapse.metrics.background_process_metrics import (
+    run_as_background_process,
+    wrap_as_background_process,
+)
 from synapse.types import JsonDict, ReadReceipt, RoomStreamToken
+from synapse.util import Clock
 from synapse.util.metrics import Measure
 
 if TYPE_CHECKING:
@@ -137,6 +144,84 @@ class AbstractFederationSender(metaclass=abc.ABCMeta):
         raise NotImplementedError()
 
 
+@attr.s
+class _PresenceQueue:
+    """A queue of destinations that need to be woken up due to new presence
+    updates.
+
+    Staggers waking up of per destination queues to ensure that we don't attempt
+    to start TLS connections with many hosts all at once, leading to pinned CPU.
+    """
+
+    # The maximum duration in seconds between queuing up a destination and it
+    # being woken up.
+    _MAX_TIME_IN_QUEUE = 30.0
+
+    # The maximum duration in seconds between waking up consecutive destination
+    # queues.
+    _MAX_DELAY = 0.1
+
+    sender: "FederationSender" = attr.ib()
+    clock: Clock = attr.ib()
+    queue: "OrderedDict[str, Literal[None]]" = attr.ib(factory=OrderedDict)
+    processing: bool = attr.ib(default=False)
+
+    def add_to_queue(self, destination: str) -> None:
+        """Add a destination to the queue to be woken up."""
+
+        self.queue[destination] = None
+
+        if not self.processing:
+            self._handle()
+
+    @wrap_as_background_process("_PresenceQueue.handle")
+    async def _handle(self) -> None:
+        """Background process to drain the queue."""
+
+        if not self.queue:
+            return
+
+        assert not self.processing
+        self.processing = True
+
+        try:
+            # We start with a delay that should drain the queue quickly enough that
+            # we process all destinations in the queue in _MAX_TIME_IN_QUEUE
+            # seconds.
+            #
+            # We also add an upper bound to the delay, to gracefully handle the
+            # case where the queue only has a few entries in it.
+            current_sleep_seconds = min(
+                self._MAX_DELAY, self._MAX_TIME_IN_QUEUE / len(self.queue)
+            )
+
+            while self.queue:
+                destination, _ = self.queue.popitem(last=False)
+
+                queue = self.sender._get_per_destination_queue(destination)
+
+                if not queue._new_data_to_send:
+                    # The per destination queue has already been woken up.
+                    continue
+
+                queue.attempt_new_transaction()
+
+                await self.clock.sleep(current_sleep_seconds)
+
+                if not self.queue:
+                    break
+
+                # More destinations may have been added to the queue, so we may
+                # need to reduce the delay to ensure everything gets processed
+                # within _MAX_TIME_IN_QUEUE seconds.
+                current_sleep_seconds = min(
+                    current_sleep_seconds, self._MAX_TIME_IN_QUEUE / len(self.queue)
+                )
+
+        finally:
+            self.processing = False
+
+
 class FederationSender(AbstractFederationSender):
     def __init__(self, hs: "HomeServer"):
         self.hs = hs
@@ -148,14 +233,14 @@ class FederationSender(AbstractFederationSender):
         self.clock = hs.get_clock()
         self.is_mine_id = hs.is_mine_id
 
-        self._presence_router = None  # type: Optional[PresenceRouter]
+        self._presence_router: Optional["PresenceRouter"] = None
         self._transaction_manager = TransactionManager(hs)
 
         self._instance_name = hs.get_instance_name()
         self._federation_shard_config = hs.config.worker.federation_shard_config
 
         # map from destination to PerDestinationQueue
-        self._per_destination_queues = {}  # type: Dict[str, PerDestinationQueue]
+        self._per_destination_queues: Dict[str, PerDestinationQueue] = {}
 
         LaterGauge(
             "synapse_federation_transaction_queue_pending_destinations",
@@ -192,9 +277,7 @@ class FederationSender(AbstractFederationSender):
         # awaiting a call to flush_read_receipts_for_room. The presence of an entry
         # here for a given room means that we are rate-limiting RR flushes to that room,
         # and that there is a pending call to _flush_rrs_for_room in the system.
-        self._queues_awaiting_rr_flush_by_room = (
-            {}
-        )  # type: Dict[str, Set[PerDestinationQueue]]
+        self._queues_awaiting_rr_flush_by_room: Dict[str, Set[PerDestinationQueue]] = {}
 
         self._rr_txn_interval_per_room_ms = (
             1000.0 / hs.config.federation_rr_transactions_per_room_per_second
@@ -210,6 +293,8 @@ class FederationSender(AbstractFederationSender):
 
         self._external_cache = hs.get_external_cache()
 
+        self._presence_queue = _PresenceQueue(self, self.clock)
+
     def _get_per_destination_queue(self, destination: str) -> PerDestinationQueue:
         """Get or create a PerDestinationQueue for the given destination
 
@@ -265,7 +350,7 @@ class FederationSender(AbstractFederationSender):
                     if not event.internal_metadata.should_proactively_send():
                         return
 
-                    destinations = None  # type: Optional[Set[str]]
+                    destinations: Optional[Set[str]] = None
                     if not event.prev_event_ids():
                         # If there are no prev event IDs then the state is empty
                         # and so no remote servers in the room
@@ -331,7 +416,7 @@ class FederationSender(AbstractFederationSender):
                         for event in events:
                             await handle_event(event)
 
-                events_by_room = {}  # type: Dict[str, List[EventBase]]
+                events_by_room: Dict[str, List[EventBase]] = {}
                 for event in events:
                     events_by_room.setdefault(event.room_id, []).append(event)
 
@@ -519,7 +604,12 @@ class FederationSender(AbstractFederationSender):
                 self._instance_name, destination
             ):
                 continue
-            self._get_per_destination_queue(destination).send_presence(states)
+
+            self._get_per_destination_queue(destination).send_presence(
+                states, start_loop=False
+            )
+
+            self._presence_queue.add_to_queue(destination)
 
     def build_and_send_edu(
         self,
@@ -628,7 +718,7 @@ class FederationSender(AbstractFederationSender):
         In order to reduce load spikes, adds a delay between each destination.
         """
 
-        last_processed = None  # type: Optional[str]
+        last_processed: Optional[str] = None
 
         while True:
             destinations_to_wake = (
diff --git a/synapse/federation/sender/per_destination_queue.py b/synapse/federation/sender/per_destination_queue.py
index 3a2efd56ee..c11d1f6d31 100644
--- a/synapse/federation/sender/per_destination_queue.py
+++ b/synapse/federation/sender/per_destination_queue.py
@@ -105,34 +105,34 @@ class PerDestinationQueue:
         # catch-up at startup.
         # New events will only be sent once this is finished, at which point
         # _catching_up is flipped to False.
-        self._catching_up = True  # type: bool
+        self._catching_up: bool = True
 
         # The stream_ordering of the most recent PDU that was discarded due to
         # being in catch-up mode.
-        self._catchup_last_skipped = 0  # type: int
+        self._catchup_last_skipped: int = 0
 
         # Cache of the last successfully-transmitted stream ordering for this
         # destination (we are the only updater so this is safe)
-        self._last_successful_stream_ordering = None  # type: Optional[int]
+        self._last_successful_stream_ordering: Optional[int] = None
 
         # a queue of pending PDUs
-        self._pending_pdus = []  # type: List[EventBase]
+        self._pending_pdus: List[EventBase] = []
 
         # XXX this is never actually used: see
         # https://github.com/matrix-org/synapse/issues/7549
-        self._pending_edus = []  # type: List[Edu]
+        self._pending_edus: List[Edu] = []
 
         # Pending EDUs by their "key". Keyed EDUs are EDUs that get clobbered
         # based on their key (e.g. typing events by room_id)
         # Map of (edu_type, key) -> Edu
-        self._pending_edus_keyed = {}  # type: Dict[Tuple[str, Hashable], Edu]
+        self._pending_edus_keyed: Dict[Tuple[str, Hashable], Edu] = {}
 
         # Map of user_id -> UserPresenceState of pending presence to be sent to this
         # destination
-        self._pending_presence = {}  # type: Dict[str, UserPresenceState]
+        self._pending_presence: Dict[str, UserPresenceState] = {}
 
         # room_id -> receipt_type -> user_id -> receipt_dict
-        self._pending_rrs = {}  # type: Dict[str, Dict[str, Dict[str, dict]]]
+        self._pending_rrs: Dict[str, Dict[str, Dict[str, dict]]] = {}
         self._rrs_pending_flush = False
 
         # stream_id of last successfully sent to-device message.
@@ -171,14 +171,24 @@ class PerDestinationQueue:
 
         self.attempt_new_transaction()
 
-    def send_presence(self, states: Iterable[UserPresenceState]) -> None:
-        """Add presence updates to the queue. Start the transmission loop if necessary.
+    def send_presence(
+        self, states: Iterable[UserPresenceState], start_loop: bool = True
+    ) -> None:
+        """Add presence updates to the queue.
+
+        Args:
+            states: Presence updates to send
+            start_loop: Whether to start the transmission loop if not already
+                running.
 
         Args:
             states: presence to send
         """
         self._pending_presence.update({state.user_id: state for state in states})
-        self.attempt_new_transaction()
+        self._new_data_to_send = True
+
+        if start_loop:
+            self.attempt_new_transaction()
 
     def queue_read_receipt(self, receipt: ReadReceipt) -> None:
         """Add a RR to the list to be sent. Doesn't start the transmission loop yet
@@ -243,7 +253,7 @@ class PerDestinationQueue:
         )
 
     async def _transaction_transmission_loop(self) -> None:
-        pending_pdus = []  # type: List[EventBase]
+        pending_pdus: List[EventBase] = []
         try:
             self.transmission_loop_running = True
 
diff --git a/synapse/federation/transport/client.py b/synapse/federation/transport/client.py
index c9e7c57461..98b1bf77fd 100644
--- a/synapse/federation/transport/client.py
+++ b/synapse/federation/transport/client.py
@@ -395,9 +395,9 @@ class TransportLayerClient:
             # this uses MSC2197 (Search Filtering over Federation)
             path = _create_v1_path("/publicRooms")
 
-            data = {
+            data: Dict[str, Any] = {
                 "include_all_networks": "true" if include_all_networks else "false"
-            }  # type: Dict[str, Any]
+            }
             if third_party_instance_id:
                 data["third_party_instance_id"] = third_party_instance_id
             if limit:
@@ -423,9 +423,9 @@ class TransportLayerClient:
         else:
             path = _create_v1_path("/publicRooms")
 
-            args = {
+            args: Dict[str, Any] = {
                 "include_all_networks": "true" if include_all_networks else "false"
-            }  # type: Dict[str, Any]
+            }
             if third_party_instance_id:
                 args["third_party_instance_id"] = (third_party_instance_id,)
             if limit:
diff --git a/synapse/federation/transport/server.py b/synapse/federation/transport/server.py
index d37d9565fc..2974d4d0cc 100644
--- a/synapse/federation/transport/server.py
+++ b/synapse/federation/transport/server.py
@@ -1013,7 +1013,7 @@ class PublicRoomList(BaseFederationServlet):
         if not self.allow_access:
             raise FederationDeniedError(origin)
 
-        limit = int(content.get("limit", 100))  # type: Optional[int]
+        limit: Optional[int] = int(content.get("limit", 100))
         since_token = content.get("since", None)
         search_filter = content.get("filter", None)
 
@@ -1095,7 +1095,9 @@ class FederationGroupsProfileServlet(BaseGroupsServerServlet):
         query: Dict[bytes, List[bytes]],
         group_id: str,
     ) -> Tuple[int, JsonDict]:
-        requester_user_id = parse_string_from_args(query, "requester_user_id")
+        requester_user_id = parse_string_from_args(
+            query, "requester_user_id", required=True
+        )
         if get_domain_from_id(requester_user_id) != origin:
             raise SynapseError(403, "requester_user_id doesn't match origin")
 
@@ -1110,7 +1112,9 @@ class FederationGroupsProfileServlet(BaseGroupsServerServlet):
         query: Dict[bytes, List[bytes]],
         group_id: str,
     ) -> Tuple[int, JsonDict]:
-        requester_user_id = parse_string_from_args(query, "requester_user_id")
+        requester_user_id = parse_string_from_args(
+            query, "requester_user_id", required=True
+        )
         if get_domain_from_id(requester_user_id) != origin:
             raise SynapseError(403, "requester_user_id doesn't match origin")
 
@@ -1131,7 +1135,9 @@ class FederationGroupsSummaryServlet(BaseGroupsServerServlet):
         query: Dict[bytes, List[bytes]],
         group_id: str,
     ) -> Tuple[int, JsonDict]:
-        requester_user_id = parse_string_from_args(query, "requester_user_id")
+        requester_user_id = parse_string_from_args(
+            query, "requester_user_id", required=True
+        )
         if get_domain_from_id(requester_user_id) != origin:
             raise SynapseError(403, "requester_user_id doesn't match origin")
 
@@ -1152,7 +1158,9 @@ class FederationGroupsRoomsServlet(BaseGroupsServerServlet):
         query: Dict[bytes, List[bytes]],
         group_id: str,
     ) -> Tuple[int, JsonDict]:
-        requester_user_id = parse_string_from_args(query, "requester_user_id")
+        requester_user_id = parse_string_from_args(
+            query, "requester_user_id", required=True
+        )
         if get_domain_from_id(requester_user_id) != origin:
             raise SynapseError(403, "requester_user_id doesn't match origin")
 
@@ -1174,7 +1182,9 @@ class FederationGroupsAddRoomsServlet(BaseGroupsServerServlet):
         group_id: str,
         room_id: str,
     ) -> Tuple[int, JsonDict]:
-        requester_user_id = parse_string_from_args(query, "requester_user_id")
+        requester_user_id = parse_string_from_args(
+            query, "requester_user_id", required=True
+        )
         if get_domain_from_id(requester_user_id) != origin:
             raise SynapseError(403, "requester_user_id doesn't match origin")
 
@@ -1192,7 +1202,9 @@ class FederationGroupsAddRoomsServlet(BaseGroupsServerServlet):
         group_id: str,
         room_id: str,
     ) -> Tuple[int, JsonDict]:
-        requester_user_id = parse_string_from_args(query, "requester_user_id")
+        requester_user_id = parse_string_from_args(
+            query, "requester_user_id", required=True
+        )
         if get_domain_from_id(requester_user_id) != origin:
             raise SynapseError(403, "requester_user_id doesn't match origin")
 
@@ -1220,7 +1232,9 @@ class FederationGroupsAddRoomsConfigServlet(BaseGroupsServerServlet):
         room_id: str,
         config_key: str,
     ) -> Tuple[int, JsonDict]:
-        requester_user_id = parse_string_from_args(query, "requester_user_id")
+        requester_user_id = parse_string_from_args(
+            query, "requester_user_id", required=True
+        )
         if get_domain_from_id(requester_user_id) != origin:
             raise SynapseError(403, "requester_user_id doesn't match origin")
 
@@ -1243,7 +1257,9 @@ class FederationGroupsUsersServlet(BaseGroupsServerServlet):
         query: Dict[bytes, List[bytes]],
         group_id: str,
     ) -> Tuple[int, JsonDict]:
-        requester_user_id = parse_string_from_args(query, "requester_user_id")
+        requester_user_id = parse_string_from_args(
+            query, "requester_user_id", required=True
+        )
         if get_domain_from_id(requester_user_id) != origin:
             raise SynapseError(403, "requester_user_id doesn't match origin")
 
@@ -1264,7 +1280,9 @@ class FederationGroupsInvitedUsersServlet(BaseGroupsServerServlet):
         query: Dict[bytes, List[bytes]],
         group_id: str,
     ) -> Tuple[int, JsonDict]:
-        requester_user_id = parse_string_from_args(query, "requester_user_id")
+        requester_user_id = parse_string_from_args(
+            query, "requester_user_id", required=True
+        )
         if get_domain_from_id(requester_user_id) != origin:
             raise SynapseError(403, "requester_user_id doesn't match origin")
 
@@ -1288,7 +1306,9 @@ class FederationGroupsInviteServlet(BaseGroupsServerServlet):
         group_id: str,
         user_id: str,
     ) -> Tuple[int, JsonDict]:
-        requester_user_id = parse_string_from_args(query, "requester_user_id")
+        requester_user_id = parse_string_from_args(
+            query, "requester_user_id", required=True
+        )
         if get_domain_from_id(requester_user_id) != origin:
             raise SynapseError(403, "requester_user_id doesn't match origin")
 
@@ -1354,7 +1374,9 @@ class FederationGroupsRemoveUserServlet(BaseGroupsServerServlet):
         group_id: str,
         user_id: str,
     ) -> Tuple[int, JsonDict]:
-        requester_user_id = parse_string_from_args(query, "requester_user_id")
+        requester_user_id = parse_string_from_args(
+            query, "requester_user_id", required=True
+        )
         if get_domain_from_id(requester_user_id) != origin:
             raise SynapseError(403, "requester_user_id doesn't match origin")
 
@@ -1487,7 +1509,9 @@ class FederationGroupsSummaryRoomsServlet(BaseGroupsServerServlet):
         category_id: str,
         room_id: str,
     ) -> Tuple[int, JsonDict]:
-        requester_user_id = parse_string_from_args(query, "requester_user_id")
+        requester_user_id = parse_string_from_args(
+            query, "requester_user_id", required=True
+        )
         if get_domain_from_id(requester_user_id) != origin:
             raise SynapseError(403, "requester_user_id doesn't match origin")
 
@@ -1523,7 +1547,9 @@ class FederationGroupsSummaryRoomsServlet(BaseGroupsServerServlet):
         category_id: str,
         room_id: str,
     ) -> Tuple[int, JsonDict]:
-        requester_user_id = parse_string_from_args(query, "requester_user_id")
+        requester_user_id = parse_string_from_args(
+            query, "requester_user_id", required=True
+        )
         if get_domain_from_id(requester_user_id) != origin:
             raise SynapseError(403, "requester_user_id doesn't match origin")
 
@@ -1549,7 +1575,9 @@ class FederationGroupsCategoriesServlet(BaseGroupsServerServlet):
         query: Dict[bytes, List[bytes]],
         group_id: str,
     ) -> Tuple[int, JsonDict]:
-        requester_user_id = parse_string_from_args(query, "requester_user_id")
+        requester_user_id = parse_string_from_args(
+            query, "requester_user_id", required=True
+        )
         if get_domain_from_id(requester_user_id) != origin:
             raise SynapseError(403, "requester_user_id doesn't match origin")
 
@@ -1571,7 +1599,9 @@ class FederationGroupsCategoryServlet(BaseGroupsServerServlet):
         group_id: str,
         category_id: str,
     ) -> Tuple[int, JsonDict]:
-        requester_user_id = parse_string_from_args(query, "requester_user_id")
+        requester_user_id = parse_string_from_args(
+            query, "requester_user_id", required=True
+        )
         if get_domain_from_id(requester_user_id) != origin:
             raise SynapseError(403, "requester_user_id doesn't match origin")
 
@@ -1589,7 +1619,9 @@ class FederationGroupsCategoryServlet(BaseGroupsServerServlet):
         group_id: str,
         category_id: str,
     ) -> Tuple[int, JsonDict]:
-        requester_user_id = parse_string_from_args(query, "requester_user_id")
+        requester_user_id = parse_string_from_args(
+            query, "requester_user_id", required=True
+        )
         if get_domain_from_id(requester_user_id) != origin:
             raise SynapseError(403, "requester_user_id doesn't match origin")
 
@@ -1618,7 +1650,9 @@ class FederationGroupsCategoryServlet(BaseGroupsServerServlet):
         group_id: str,
         category_id: str,
     ) -> Tuple[int, JsonDict]:
-        requester_user_id = parse_string_from_args(query, "requester_user_id")
+        requester_user_id = parse_string_from_args(
+            query, "requester_user_id", required=True
+        )
         if get_domain_from_id(requester_user_id) != origin:
             raise SynapseError(403, "requester_user_id doesn't match origin")
 
@@ -1644,7 +1678,9 @@ class FederationGroupsRolesServlet(BaseGroupsServerServlet):
         query: Dict[bytes, List[bytes]],
         group_id: str,
     ) -> Tuple[int, JsonDict]:
-        requester_user_id = parse_string_from_args(query, "requester_user_id")
+        requester_user_id = parse_string_from_args(
+            query, "requester_user_id", required=True
+        )
         if get_domain_from_id(requester_user_id) != origin:
             raise SynapseError(403, "requester_user_id doesn't match origin")
 
@@ -1666,7 +1702,9 @@ class FederationGroupsRoleServlet(BaseGroupsServerServlet):
         group_id: str,
         role_id: str,
     ) -> Tuple[int, JsonDict]:
-        requester_user_id = parse_string_from_args(query, "requester_user_id")
+        requester_user_id = parse_string_from_args(
+            query, "requester_user_id", required=True
+        )
         if get_domain_from_id(requester_user_id) != origin:
             raise SynapseError(403, "requester_user_id doesn't match origin")
 
@@ -1682,7 +1720,9 @@ class FederationGroupsRoleServlet(BaseGroupsServerServlet):
         group_id: str,
         role_id: str,
     ) -> Tuple[int, JsonDict]:
-        requester_user_id = parse_string_from_args(query, "requester_user_id")
+        requester_user_id = parse_string_from_args(
+            query, "requester_user_id", required=True
+        )
         if get_domain_from_id(requester_user_id) != origin:
             raise SynapseError(403, "requester_user_id doesn't match origin")
 
@@ -1713,7 +1753,9 @@ class FederationGroupsRoleServlet(BaseGroupsServerServlet):
         group_id: str,
         role_id: str,
     ) -> Tuple[int, JsonDict]:
-        requester_user_id = parse_string_from_args(query, "requester_user_id")
+        requester_user_id = parse_string_from_args(
+            query, "requester_user_id", required=True
+        )
         if get_domain_from_id(requester_user_id) != origin:
             raise SynapseError(403, "requester_user_id doesn't match origin")
 
@@ -1750,7 +1792,9 @@ class FederationGroupsSummaryUsersServlet(BaseGroupsServerServlet):
         role_id: str,
         user_id: str,
     ) -> Tuple[int, JsonDict]:
-        requester_user_id = parse_string_from_args(query, "requester_user_id")
+        requester_user_id = parse_string_from_args(
+            query, "requester_user_id", required=True
+        )
         if get_domain_from_id(requester_user_id) != origin:
             raise SynapseError(403, "requester_user_id doesn't match origin")
 
@@ -1784,7 +1828,9 @@ class FederationGroupsSummaryUsersServlet(BaseGroupsServerServlet):
         role_id: str,
         user_id: str,
     ) -> Tuple[int, JsonDict]:
-        requester_user_id = parse_string_from_args(query, "requester_user_id")
+        requester_user_id = parse_string_from_args(
+            query, "requester_user_id", required=True
+        )
         if get_domain_from_id(requester_user_id) != origin:
             raise SynapseError(403, "requester_user_id doesn't match origin")
 
@@ -1825,7 +1871,9 @@ class FederationGroupsSettingJoinPolicyServlet(BaseGroupsServerServlet):
         query: Dict[bytes, List[bytes]],
         group_id: str,
     ) -> Tuple[int, JsonDict]:
-        requester_user_id = parse_string_from_args(query, "requester_user_id")
+        requester_user_id = parse_string_from_args(
+            query, "requester_user_id", required=True
+        )
         if get_domain_from_id(requester_user_id) != origin:
             raise SynapseError(403, "requester_user_id doesn't match origin")
 
@@ -1943,7 +1991,7 @@ class RoomComplexityServlet(BaseFederationServlet):
         return 200, complexity
 
 
-FEDERATION_SERVLET_CLASSES = (
+FEDERATION_SERVLET_CLASSES: Tuple[Type[BaseFederationServlet], ...] = (
     FederationSendServlet,
     FederationEventServlet,
     FederationStateV1Servlet,
@@ -1971,15 +2019,13 @@ FEDERATION_SERVLET_CLASSES = (
     FederationSpaceSummaryServlet,
     FederationV1SendKnockServlet,
     FederationMakeKnockServlet,
-)  # type: Tuple[Type[BaseFederationServlet], ...]
+)
 
-OPENID_SERVLET_CLASSES = (
-    OpenIdUserInfo,
-)  # type: Tuple[Type[BaseFederationServlet], ...]
+OPENID_SERVLET_CLASSES: Tuple[Type[BaseFederationServlet], ...] = (OpenIdUserInfo,)
 
-ROOM_LIST_CLASSES = (PublicRoomList,)  # type: Tuple[Type[PublicRoomList], ...]
+ROOM_LIST_CLASSES: Tuple[Type[PublicRoomList], ...] = (PublicRoomList,)
 
-GROUP_SERVER_SERVLET_CLASSES = (
+GROUP_SERVER_SERVLET_CLASSES: Tuple[Type[BaseFederationServlet], ...] = (
     FederationGroupsProfileServlet,
     FederationGroupsSummaryServlet,
     FederationGroupsRoomsServlet,
@@ -1998,19 +2044,19 @@ GROUP_SERVER_SERVLET_CLASSES = (
     FederationGroupsAddRoomsServlet,
     FederationGroupsAddRoomsConfigServlet,
     FederationGroupsSettingJoinPolicyServlet,
-)  # type: Tuple[Type[BaseFederationServlet], ...]
+)
 
 
-GROUP_LOCAL_SERVLET_CLASSES = (
+GROUP_LOCAL_SERVLET_CLASSES: Tuple[Type[BaseFederationServlet], ...] = (
     FederationGroupsLocalInviteServlet,
     FederationGroupsRemoveLocalUserServlet,
     FederationGroupsBulkPublicisedServlet,
-)  # type: Tuple[Type[BaseFederationServlet], ...]
+)
 
 
-GROUP_ATTESTATION_SERVLET_CLASSES = (
+GROUP_ATTESTATION_SERVLET_CLASSES: Tuple[Type[BaseFederationServlet], ...] = (
     FederationGroupsRenewAttestaionServlet,
-)  # type: Tuple[Type[BaseFederationServlet], ...]
+)
 
 
 DEFAULT_SERVLET_GROUPS = (
diff --git a/synapse/groups/groups_server.py b/synapse/groups/groups_server.py
index a06d060ebf..3dc55ab861 100644
--- a/synapse/groups/groups_server.py
+++ b/synapse/groups/groups_server.py
@@ -707,9 +707,9 @@ class GroupsServerHandler(GroupsServerWorkerHandler):
         See accept_invite, join_group.
         """
         if not self.hs.is_mine_id(user_id):
-            local_attestation = self.attestations.create_attestation(
-                group_id, user_id
-            )  # type: Optional[JsonDict]
+            local_attestation: Optional[
+                JsonDict
+            ] = self.attestations.create_attestation(group_id, user_id)
 
             remote_attestation = content["attestation"]
 
@@ -868,9 +868,9 @@ class GroupsServerHandler(GroupsServerWorkerHandler):
                 remote_attestation, user_id=requester_user_id, group_id=group_id
             )
 
-            local_attestation = self.attestations.create_attestation(
-                group_id, requester_user_id
-            )  # type: Optional[JsonDict]
+            local_attestation: Optional[
+                JsonDict
+            ] = self.attestations.create_attestation(group_id, requester_user_id)
         else:
             local_attestation = None
             remote_attestation = None
diff --git a/synapse/handlers/directory.py b/synapse/handlers/directory.py
index 4064a2b859..06d7012bac 100644
--- a/synapse/handlers/directory.py
+++ b/synapse/handlers/directory.py
@@ -22,6 +22,7 @@ from synapse.api.errors import (
     CodeMessageException,
     Codes,
     NotFoundError,
+    RequestSendFailed,
     ShadowBanError,
     StoreError,
     SynapseError,
@@ -252,12 +253,14 @@ class DirectoryHandler(BaseHandler):
                     retry_on_dns_fail=False,
                     ignore_backoff=True,
                 )
+            except RequestSendFailed:
+                raise SynapseError(502, "Failed to fetch alias")
             except CodeMessageException as e:
                 logging.warning("Error retrieving alias")
                 if e.code == 404:
                     fed_result = None
                 else:
-                    raise
+                    raise SynapseError(502, "Failed to fetch alias")
 
             if fed_result and "room_id" in fed_result and "servers" in fed_result:
                 room_id = fed_result["room_id"]
diff --git a/synapse/handlers/federation.py b/synapse/handlers/federation.py
index 991ec9919a..0209aee186 100644
--- a/synapse/handlers/federation.py
+++ b/synapse/handlers/federation.py
@@ -1414,12 +1414,15 @@ class FederationHandler(BaseHandler):
 
         Invites must be signed by the invitee's server before distribution.
         """
-        pdu = await self.federation_client.send_invite(
-            destination=target_host,
-            room_id=event.room_id,
-            event_id=event.event_id,
-            pdu=event,
-        )
+        try:
+            pdu = await self.federation_client.send_invite(
+                destination=target_host,
+                room_id=event.room_id,
+                event_id=event.event_id,
+                pdu=event,
+            )
+        except RequestSendFailed:
+            raise SynapseError(502, f"Can't connect to server {target_host}")
 
         return pdu
 
@@ -3031,9 +3034,13 @@ class FederationHandler(BaseHandler):
             await member_handler.send_membership_event(None, event, context)
         else:
             destinations = {x.split(":", 1)[-1] for x in (sender_user_id, room_id)}
-            await self.federation_client.forward_third_party_invite(
-                destinations, room_id, event_dict
-            )
+
+            try:
+                await self.federation_client.forward_third_party_invite(
+                    destinations, room_id, event_dict
+                )
+            except (RequestSendFailed, HttpResponseException):
+                raise SynapseError(502, "Failed to forward third party invite")
 
     async def on_exchange_third_party_invite_request(
         self, event_dict: JsonDict
diff --git a/synapse/handlers/message.py b/synapse/handlers/message.py
index 66e40a915d..e06655f3d4 100644
--- a/synapse/handlers/message.py
+++ b/synapse/handlers/message.py
@@ -518,6 +518,9 @@ class EventCreationHandler:
             outlier: Indicates whether the event is an `outlier`, i.e. if
                 it's from an arbitrary point and floating in the DAG as
                 opposed to being inline with the current DAG.
+            historical: Indicates whether the message is being inserted
+                back in time around some existing events. This is used to skip
+                a few checks and mark the event as backfilled.
             depth: Override the depth used to order the event in the DAG.
                 Should normally be set to None, which will cause the depth to be calculated
                 based on the prev_events.
@@ -772,6 +775,7 @@ class EventCreationHandler:
         txn_id: Optional[str] = None,
         ignore_shadow_ban: bool = False,
         outlier: bool = False,
+        historical: bool = False,
         depth: Optional[int] = None,
     ) -> Tuple[EventBase, int]:
         """
@@ -799,6 +803,9 @@ class EventCreationHandler:
             outlier: Indicates whether the event is an `outlier`, i.e. if
                 it's from an arbitrary point and floating in the DAG as
                 opposed to being inline with the current DAG.
+            historical: Indicates whether the message is being inserted
+                back in time around some existing events. This is used to skip
+                a few checks and mark the event as backfilled.
             depth: Override the depth used to order the event in the DAG.
                 Should normally be set to None, which will cause the depth to be calculated
                 based on the prev_events.
@@ -847,6 +854,7 @@ class EventCreationHandler:
                 prev_event_ids=prev_event_ids,
                 auth_event_ids=auth_event_ids,
                 outlier=outlier,
+                historical=historical,
                 depth=depth,
             )
 
@@ -1594,11 +1602,13 @@ class EventCreationHandler:
         for k, v in original_event.internal_metadata.get_dict().items():
             setattr(builder.internal_metadata, k, v)
 
-        # the event type hasn't changed, so there's no point in re-calculating the
-        # auth events.
+        # modules can send new state events, so we re-calculate the auth events just in
+        # case.
+        prev_event_ids = await self.store.get_prev_events_for_room(builder.room_id)
+
         event = await builder.build(
-            prev_event_ids=original_event.prev_event_ids(),
-            auth_event_ids=original_event.auth_event_ids(),
+            prev_event_ids=prev_event_ids,
+            auth_event_ids=None,
         )
 
         # we rebuild the event context, to be on the safe side. If nothing else,
diff --git a/synapse/handlers/receipts.py b/synapse/handlers/receipts.py
index f782d9db32..0059ad0f56 100644
--- a/synapse/handlers/receipts.py
+++ b/synapse/handlers/receipts.py
@@ -30,6 +30,8 @@ class ReceiptsHandler(BaseHandler):
 
         self.server_name = hs.config.server_name
         self.store = hs.get_datastore()
+        self.event_auth_handler = hs.get_event_auth_handler()
+
         self.hs = hs
 
         # We only need to poke the federation sender explicitly if its on the
@@ -59,6 +61,19 @@ class ReceiptsHandler(BaseHandler):
         """Called when we receive an EDU of type m.receipt from a remote HS."""
         receipts = []
         for room_id, room_values in content.items():
+            # If we're not in the room just ditch the event entirely. This is
+            # probably an old server that has come back and thinks we're still in
+            # the room (or we've been rejoined to the room by a state reset).
+            is_in_room = await self.event_auth_handler.check_host_in_room(
+                room_id, self.server_name
+            )
+            if not is_in_room:
+                logger.info(
+                    "Ignoring receipt from %s as we're not in the room",
+                    origin,
+                )
+                continue
+
             for receipt_type, users in room_values.items():
                 for user_id, user_values in users.items():
                     if get_domain_from_id(user_id) != origin:
diff --git a/synapse/handlers/room_list.py b/synapse/handlers/room_list.py
index 5e3ef7ce3a..c6bfa5451f 100644
--- a/synapse/handlers/room_list.py
+++ b/synapse/handlers/room_list.py
@@ -20,7 +20,12 @@ import msgpack
 from unpaddedbase64 import decode_base64, encode_base64
 
 from synapse.api.constants import EventTypes, HistoryVisibility, JoinRules
-from synapse.api.errors import Codes, HttpResponseException
+from synapse.api.errors import (
+    Codes,
+    HttpResponseException,
+    RequestSendFailed,
+    SynapseError,
+)
 from synapse.types import JsonDict, ThirdPartyInstanceID
 from synapse.util.caches.descriptors import cached
 from synapse.util.caches.response_cache import ResponseCache
@@ -417,14 +422,17 @@ class RoomListHandler(BaseHandler):
         repl_layer = self.hs.get_federation_client()
         if search_filter:
             # We can't cache when asking for search
-            return await repl_layer.get_public_rooms(
-                server_name,
-                limit=limit,
-                since_token=since_token,
-                search_filter=search_filter,
-                include_all_networks=include_all_networks,
-                third_party_instance_id=third_party_instance_id,
-            )
+            try:
+                return await repl_layer.get_public_rooms(
+                    server_name,
+                    limit=limit,
+                    since_token=since_token,
+                    search_filter=search_filter,
+                    include_all_networks=include_all_networks,
+                    third_party_instance_id=third_party_instance_id,
+                )
+            except (RequestSendFailed, HttpResponseException):
+                raise SynapseError(502, "Failed to fetch room list")
 
         key = (
             server_name,
diff --git a/synapse/handlers/space_summary.py b/synapse/handlers/space_summary.py
index b585057ec3..366e6211e5 100644
--- a/synapse/handlers/space_summary.py
+++ b/synapse/handlers/space_summary.py
@@ -24,6 +24,7 @@ from synapse.api.constants import (
     EventContentFields,
     EventTypes,
     HistoryVisibility,
+    JoinRules,
     Membership,
     RoomTypes,
 )
@@ -150,14 +151,21 @@ class SpaceSummaryHandler:
                     # The room should only be included in the summary if:
                     #     a. the user is in the room;
                     #     b. the room is world readable; or
-                    #     c. the user is in a space that has been granted access to
-                    #        the room.
+                    #     c. the user could join the room, e.g. the join rules
+                    #        are set to public or the user is in a space that
+                    #        has been granted access to the room.
                     #
                     # Note that we know the user is not in the root room (which is
                     # why the remote call was made in the first place), but the user
                     # could be in one of the children rooms and we just didn't know
                     # about the link.
-                    include_room = room.get("world_readable") is True
+
+                    # The API doesn't return the room version so assume that a
+                    # join rule of knock is valid.
+                    include_room = (
+                        room.get("join_rules") in (JoinRules.PUBLIC, JoinRules.KNOCK)
+                        or room.get("world_readable") is True
+                    )
 
                     # Check if the user is a member of any of the allowed spaces
                     # from the response.
@@ -420,9 +428,8 @@ class SpaceSummaryHandler:
 
         It should be included if:
 
-        * The requester is joined or invited to the room.
-        * The requester can join without an invite (per MSC3083).
-        * The origin server has any user that is joined or invited to the room.
+        * The requester is joined or can join the room (per MSC3173).
+        * The origin server has any user that is joined or can join the room.
         * The history visibility is set to world readable.
 
         Args:
@@ -441,13 +448,39 @@ class SpaceSummaryHandler:
 
         # If there's no state for the room, it isn't known.
         if not state_ids:
+            # The user might have a pending invite for the room.
+            if requester and await self._store.get_invite_for_local_user_in_room(
+                requester, room_id
+            ):
+                return True
+
             logger.info("room %s is unknown, omitting from summary", room_id)
             return False
 
         room_version = await self._store.get_room_version(room_id)
 
-        # if we have an authenticated requesting user, first check if they are able to view
-        # stripped state in the room.
+        # Include the room if it has join rules of public or knock.
+        join_rules_event_id = state_ids.get((EventTypes.JoinRules, ""))
+        if join_rules_event_id:
+            join_rules_event = await self._store.get_event(join_rules_event_id)
+            join_rule = join_rules_event.content.get("join_rule")
+            if join_rule == JoinRules.PUBLIC or (
+                room_version.msc2403_knocking and join_rule == JoinRules.KNOCK
+            ):
+                return True
+
+        # Include the room if it is peekable.
+        hist_vis_event_id = state_ids.get((EventTypes.RoomHistoryVisibility, ""))
+        if hist_vis_event_id:
+            hist_vis_ev = await self._store.get_event(hist_vis_event_id)
+            hist_vis = hist_vis_ev.content.get("history_visibility")
+            if hist_vis == HistoryVisibility.WORLD_READABLE:
+                return True
+
+        # Otherwise we need to check information specific to the user or server.
+
+        # If we have an authenticated requesting user, check if they are a member
+        # of the room (or can join the room).
         if requester:
             member_event_id = state_ids.get((EventTypes.Member, requester), None)
 
@@ -470,9 +503,11 @@ class SpaceSummaryHandler:
                     return True
 
         # If this is a request over federation, check if the host is in the room or
-        # is in one of the spaces specified via the join rules.
+        # has a user who could join the room.
         elif origin:
-            if await self._event_auth_handler.check_host_in_room(room_id, origin):
+            if await self._event_auth_handler.check_host_in_room(
+                room_id, origin
+            ) or await self._store.is_host_invited(room_id, origin):
                 return True
 
             # Alternately, if the host has a user in any of the spaces specified
@@ -490,18 +525,10 @@ class SpaceSummaryHandler:
                     ):
                         return True
 
-        # otherwise, check if the room is peekable
-        hist_vis_event_id = state_ids.get((EventTypes.RoomHistoryVisibility, ""), None)
-        if hist_vis_event_id:
-            hist_vis_ev = await self._store.get_event(hist_vis_event_id)
-            hist_vis = hist_vis_ev.content.get("history_visibility")
-            if hist_vis == HistoryVisibility.WORLD_READABLE:
-                return True
-
         logger.info(
-            "room %s is unpeekable and user %s is not a member / not allowed to join, omitting from summary",
+            "room %s is unpeekable and requester %s is not a member / not allowed to join, omitting from summary",
             room_id,
-            requester,
+            requester or origin,
         )
         return False
 
@@ -535,6 +562,7 @@ class SpaceSummaryHandler:
             "canonical_alias": stats["canonical_alias"],
             "num_joined_members": stats["joined_members"],
             "avatar_url": stats["avatar"],
+            "join_rules": stats["join_rules"],
             "world_readable": (
                 stats["history_visibility"] == HistoryVisibility.WORLD_READABLE
             ),
diff --git a/synapse/handlers/stats.py b/synapse/handlers/stats.py
index 4e45d1da57..814d08efcb 100644
--- a/synapse/handlers/stats.py
+++ b/synapse/handlers/stats.py
@@ -45,7 +45,6 @@ class StatsHandler:
         self.clock = hs.get_clock()
         self.notifier = hs.get_notifier()
         self.is_mine_id = hs.is_mine_id
-        self.stats_bucket_size = hs.config.stats_bucket_size
 
         self.stats_enabled = hs.config.stats_enabled
 
@@ -106,20 +105,6 @@ class StatsHandler:
                 room_deltas = {}
                 user_deltas = {}
 
-            # Then count deltas for total_events and total_event_bytes.
-            (
-                room_count,
-                user_count,
-            ) = await self.store.get_changes_room_total_events_and_bytes(
-                self.pos, max_pos
-            )
-
-            for room_id, fields in room_count.items():
-                room_deltas.setdefault(room_id, Counter()).update(fields)
-
-            for user_id, fields in user_count.items():
-                user_deltas.setdefault(user_id, Counter()).update(fields)
-
             logger.debug("room_deltas: %s", room_deltas)
             logger.debug("user_deltas: %s", user_deltas)
 
@@ -181,12 +166,10 @@ class StatsHandler:
 
             event_content = {}  # type: JsonDict
 
-            sender = None
             if event_id is not None:
                 event = await self.store.get_event(event_id, allow_none=True)
                 if event:
                     event_content = event.content or {}
-                    sender = event.sender
 
             # All the values in this dict are deltas (RELATIVE changes)
             room_stats_delta = room_to_stats_deltas.setdefault(room_id, Counter())
@@ -244,12 +227,6 @@ class StatsHandler:
                     room_stats_delta["joined_members"] += 1
                 elif membership == Membership.INVITE:
                     room_stats_delta["invited_members"] += 1
-
-                    if sender and self.is_mine_id(sender):
-                        user_to_stats_deltas.setdefault(sender, Counter())[
-                            "invites_sent"
-                        ] += 1
-
                 elif membership == Membership.LEAVE:
                     room_stats_delta["left_members"] += 1
                 elif membership == Membership.BAN:
@@ -279,10 +256,6 @@ class StatsHandler:
                 room_state["is_federatable"] = (
                     event_content.get("m.federate", True) is True
                 )
-                if sender and self.is_mine_id(sender):
-                    user_to_stats_deltas.setdefault(sender, Counter())[
-                        "rooms_created"
-                    ] += 1
             elif typ == EventTypes.JoinRules:
                 room_state["join_rules"] = event_content.get("join_rule")
             elif typ == EventTypes.RoomHistoryVisibility:
diff --git a/synapse/handlers/typing.py b/synapse/handlers/typing.py
index e22393adc4..c0a8364755 100644
--- a/synapse/handlers/typing.py
+++ b/synapse/handlers/typing.py
@@ -208,6 +208,7 @@ class TypingWriterHandler(FollowerTypingHandler):
 
         self.auth = hs.get_auth()
         self.notifier = hs.get_notifier()
+        self.event_auth_handler = hs.get_event_auth_handler()
 
         self.hs = hs
 
@@ -326,6 +327,19 @@ class TypingWriterHandler(FollowerTypingHandler):
         room_id = content["room_id"]
         user_id = content["user_id"]
 
+        # If we're not in the room just ditch the event entirely. This is
+        # probably an old server that has come back and thinks we're still in
+        # the room (or we've been rejoined to the room by a state reset).
+        is_in_room = await self.event_auth_handler.check_host_in_room(
+            room_id, self.server_name
+        )
+        if not is_in_room:
+            logger.info(
+                "Ignoring typing update from %s as we're not in the room",
+                origin,
+            )
+            return
+
         member = RoomMember(user_id=user_id, room_id=room_id)
 
         # Check that the string is a valid user id
diff --git a/synapse/http/__init__.py b/synapse/http/__init__.py
index ed4671b7de..578fc48ef4 100644
--- a/synapse/http/__init__.py
+++ b/synapse/http/__init__.py
@@ -69,7 +69,7 @@ def _get_requested_host(request: IRequest) -> bytes:
         return hostname
 
     # no Host header, use the address/port that the request arrived on
-    host = request.getHost()  # type: Union[address.IPv4Address, address.IPv6Address]
+    host: Union[address.IPv4Address, address.IPv6Address] = request.getHost()
 
     hostname = host.host.encode("ascii")
 
diff --git a/synapse/http/client.py b/synapse/http/client.py
index 1ca6624fd5..2ac76b15c2 100644
--- a/synapse/http/client.py
+++ b/synapse/http/client.py
@@ -160,7 +160,7 @@ class _IPBlacklistingResolver:
     def resolveHostName(
         self, recv: IResolutionReceiver, hostname: str, portNumber: int = 0
     ) -> IResolutionReceiver:
-        addresses = []  # type: List[IAddress]
+        addresses: List[IAddress] = []
 
         def _callback() -> None:
             has_bad_ip = False
@@ -333,9 +333,9 @@ class SimpleHttpClient:
         if self._ip_blacklist:
             # If we have an IP blacklist, we need to use a DNS resolver which
             # filters out blacklisted IP addresses, to prevent DNS rebinding.
-            self.reactor = BlacklistingReactorWrapper(
+            self.reactor: ISynapseReactor = BlacklistingReactorWrapper(
                 hs.get_reactor(), self._ip_whitelist, self._ip_blacklist
-            )  # type: ISynapseReactor
+            )
         else:
             self.reactor = hs.get_reactor()
 
@@ -349,14 +349,14 @@ class SimpleHttpClient:
         pool.maxPersistentPerHost = max((100 * hs.config.caches.global_factor, 5))
         pool.cachedConnectionTimeout = 2 * 60
 
-        self.agent = ProxyAgent(
+        self.agent: IAgent = ProxyAgent(
             self.reactor,
             hs.get_reactor(),
             connectTimeout=15,
             contextFactory=self.hs.get_http_client_context_factory(),
             pool=pool,
             use_proxy=use_proxy,
-        )  # type: IAgent
+        )
 
         if self._ip_blacklist:
             # If we have an IP blacklist, we then install the blacklisting Agent
@@ -411,7 +411,7 @@ class SimpleHttpClient:
                         cooperator=self._cooperator,
                     )
 
-                request_deferred = treq.request(
+                request_deferred: defer.Deferred = treq.request(
                     method,
                     uri,
                     agent=self.agent,
@@ -421,7 +421,7 @@ class SimpleHttpClient:
                     # response bodies.
                     unbuffered=True,
                     **self._extra_treq_args,
-                )  # type: defer.Deferred
+                )
 
                 # we use our own timeout mechanism rather than treq's as a workaround
                 # for https://twistedmatrix.com/trac/ticket/9534.
@@ -772,7 +772,7 @@ class BodyExceededMaxSize(Exception):
 class _DiscardBodyWithMaxSizeProtocol(protocol.Protocol):
     """A protocol which immediately errors upon receiving data."""
 
-    transport = None  # type: Optional[ITCPTransport]
+    transport: Optional[ITCPTransport] = None
 
     def __init__(self, deferred: defer.Deferred):
         self.deferred = deferred
@@ -798,7 +798,7 @@ class _DiscardBodyWithMaxSizeProtocol(protocol.Protocol):
 class _ReadBodyWithMaxSizeProtocol(protocol.Protocol):
     """A protocol which reads body to a stream, erroring if the body exceeds a maximum size."""
 
-    transport = None  # type: Optional[ITCPTransport]
+    transport: Optional[ITCPTransport] = None
 
     def __init__(
         self, stream: ByteWriteable, deferred: defer.Deferred, max_size: Optional[int]
diff --git a/synapse/http/matrixfederationclient.py b/synapse/http/matrixfederationclient.py
index b8849c0150..2efa15bf04 100644
--- a/synapse/http/matrixfederationclient.py
+++ b/synapse/http/matrixfederationclient.py
@@ -43,6 +43,7 @@ from twisted.internet import defer
 from twisted.internet.error import DNSLookupError
 from twisted.internet.interfaces import IReactorTime
 from twisted.internet.task import _EPSILON, Cooperator
+from twisted.web.client import ResponseFailed
 from twisted.web.http_headers import Headers
 from twisted.web.iweb import IBodyProducer, IResponse
 
@@ -105,7 +106,7 @@ class ByteParser(ByteWriteable, Generic[T], abc.ABC):
     the parsed data.
     """
 
-    CONTENT_TYPE = abc.abstractproperty()  # type: str  # type: ignore
+    CONTENT_TYPE: str = abc.abstractproperty()  # type: ignore
     """The expected content type of the response, e.g. `application/json`. If
     the content type doesn't match we fail the request.
     """
@@ -262,6 +263,15 @@ async def _handle_response(
             request.uri.decode("ascii"),
         )
         raise RequestSendFailed(e, can_retry=True) from e
+    except ResponseFailed as e:
+        logger.warning(
+            "{%s} [%s] Failed to read response - %s %s",
+            request.txn_id,
+            request.destination,
+            request.method,
+            request.uri.decode("ascii"),
+        )
+        raise RequestSendFailed(e, can_retry=True) from e
     except Exception as e:
         logger.warning(
             "{%s} [%s] Error reading response %s %s: %s",
@@ -317,11 +327,11 @@ class MatrixFederationHttpClient:
 
         # We need to use a DNS resolver which filters out blacklisted IP
         # addresses, to prevent DNS rebinding.
-        self.reactor = BlacklistingReactorWrapper(
+        self.reactor: ISynapseReactor = BlacklistingReactorWrapper(
             hs.get_reactor(),
             hs.config.federation_ip_range_whitelist,
             hs.config.federation_ip_range_blacklist,
-        )  # type: ISynapseReactor
+        )
 
         user_agent = hs.version_string
         if hs.config.user_agent_suffix:
@@ -494,7 +504,7 @@ class MatrixFederationHttpClient:
         )
 
         # Inject the span into the headers
-        headers_dict = {}  # type: Dict[bytes, List[bytes]]
+        headers_dict: Dict[bytes, List[bytes]] = {}
         opentracing.inject_header_dict(headers_dict, request.destination)
 
         headers_dict[b"User-Agent"] = [self.version_string_bytes]
@@ -523,9 +533,9 @@ class MatrixFederationHttpClient:
                             destination_bytes, method_bytes, url_to_sign_bytes, json
                         )
                         data = encode_canonical_json(json)
-                        producer = QuieterFileBodyProducer(
+                        producer: Optional[IBodyProducer] = QuieterFileBodyProducer(
                             BytesIO(data), cooperator=self._cooperator
-                        )  # type: Optional[IBodyProducer]
+                        )
                     else:
                         producer = None
                         auth_headers = self.build_auth_headers(
@@ -1137,6 +1147,24 @@ class MatrixFederationHttpClient:
                 msg,
             )
             raise SynapseError(502, msg, Codes.TOO_LARGE)
+        except defer.TimeoutError as e:
+            logger.warning(
+                "{%s} [%s] Timed out reading response - %s %s",
+                request.txn_id,
+                request.destination,
+                request.method,
+                request.uri.decode("ascii"),
+            )
+            raise RequestSendFailed(e, can_retry=True) from e
+        except ResponseFailed as e:
+            logger.warning(
+                "{%s} [%s] Failed to read response - %s %s",
+                request.txn_id,
+                request.destination,
+                request.method,
+                request.uri.decode("ascii"),
+            )
+            raise RequestSendFailed(e, can_retry=True) from e
         except Exception as e:
             logger.warning(
                 "{%s} [%s] Error reading response: %s",
diff --git a/synapse/http/proxyagent.py b/synapse/http/proxyagent.py
index 7dfae8b786..7a6a1717de 100644
--- a/synapse/http/proxyagent.py
+++ b/synapse/http/proxyagent.py
@@ -117,7 +117,8 @@ class ProxyAgent(_AgentBase):
             https_proxy = proxies["https"].encode() if "https" in proxies else None
             no_proxy = proxies["no"] if "no" in proxies else None
 
-        # Parse credentials from https proxy connection string if present
+        # Parse credentials from http and https proxy connection string if present
+        self.http_proxy_creds, http_proxy = parse_username_password(http_proxy)
         self.https_proxy_creds, https_proxy = parse_username_password(https_proxy)
 
         self.http_proxy_endpoint = _http_proxy_endpoint(
@@ -189,6 +190,15 @@ class ProxyAgent(_AgentBase):
             and self.http_proxy_endpoint
             and not should_skip_proxy
         ):
+            # Determine whether we need to set Proxy-Authorization headers
+            if self.http_proxy_creds:
+                # Set a Proxy-Authorization header
+                if headers is None:
+                    headers = Headers()
+                headers.addRawHeader(
+                    b"Proxy-Authorization",
+                    self.http_proxy_creds.as_proxy_authorization_value(),
+                )
             # Cache *all* connections under the same key, since we are only
             # connecting to a single destination, the proxy:
             pool_key = ("http-proxy", self.http_proxy_endpoint)
diff --git a/synapse/http/server.py b/synapse/http/server.py
index efbc6d5b25..b79fa722e9 100644
--- a/synapse/http/server.py
+++ b/synapse/http/server.py
@@ -81,7 +81,7 @@ def return_json_error(f: failure.Failure, request: SynapseRequest) -> None:
 
     if f.check(SynapseError):
         # mypy doesn't understand that f.check asserts the type.
-        exc = f.value  # type: SynapseError  # type: ignore
+        exc: SynapseError = f.value  # type: ignore
         error_code = exc.code
         error_dict = exc.error_dict()
 
@@ -132,7 +132,7 @@ def return_html_error(
     """
     if f.check(CodeMessageException):
         # mypy doesn't understand that f.check asserts the type.
-        cme = f.value  # type: CodeMessageException  # type: ignore
+        cme: CodeMessageException = f.value  # type: ignore
         code = cme.code
         msg = cme.msg
 
@@ -404,7 +404,7 @@ class JsonResource(DirectServeJsonResource):
             key word arguments to pass to the callback
         """
         # At this point the path must be bytes.
-        request_path_bytes = request.path  # type: bytes  # type: ignore
+        request_path_bytes: bytes = request.path  # type: ignore
         request_path = request_path_bytes.decode("ascii")
         # Treat HEAD requests as GET requests.
         request_method = request.method
@@ -557,7 +557,7 @@ class _ByteProducer:
         request: Request,
         iterator: Iterator[bytes],
     ):
-        self._request = request  # type: Optional[Request]
+        self._request: Optional[Request] = request
         self._iterator = iterator
         self._paused = False
 
diff --git a/synapse/http/servlet.py b/synapse/http/servlet.py
index 6ba2ce1e53..04560fb589 100644
--- a/synapse/http/servlet.py
+++ b/synapse/http/servlet.py
@@ -205,7 +205,7 @@ def parse_string(
             parameter is present, must be one of a list of allowed values and
             is not one of those allowed values.
     """
-    args = request.args  # type: Dict[bytes, List[bytes]]  # type: ignore
+    args: Dict[bytes, List[bytes]] = request.args  # type: ignore
     return parse_string_from_args(
         args,
         name,
diff --git a/synapse/http/site.py b/synapse/http/site.py
index 40754b7bea..3b0a38124e 100644
--- a/synapse/http/site.py
+++ b/synapse/http/site.py
@@ -64,16 +64,16 @@ class SynapseRequest(Request):
     def __init__(self, channel, *args, max_request_body_size=1024, **kw):
         Request.__init__(self, channel, *args, **kw)
         self._max_request_body_size = max_request_body_size
-        self.site = channel.site  # type: SynapseSite
+        self.site: SynapseSite = channel.site
         self._channel = channel  # this is used by the tests
         self.start_time = 0.0
 
         # The requester, if authenticated. For federation requests this is the
         # server name, for client requests this is the Requester object.
-        self._requester = None  # type: Optional[Union[Requester, str]]
+        self._requester: Optional[Union[Requester, str]] = None
 
         # we can't yet create the logcontext, as we don't know the method.
-        self.logcontext = None  # type: Optional[LoggingContext]
+        self.logcontext: Optional[LoggingContext] = None
 
         global _next_request_seq
         self.request_seq = _next_request_seq
@@ -152,7 +152,7 @@ class SynapseRequest(Request):
         Returns:
             The redacted URI as a string.
         """
-        uri = self.uri  # type: Union[bytes, str]
+        uri: Union[bytes, str] = self.uri
         if isinstance(uri, bytes):
             uri = uri.decode("ascii", errors="replace")
         return redact_uri(uri)
@@ -167,7 +167,7 @@ class SynapseRequest(Request):
         Returns:
             The request method as a string.
         """
-        method = self.method  # type: Union[bytes, str]
+        method: Union[bytes, str] = self.method
         if isinstance(method, bytes):
             return self.method.decode("ascii")
         return method
@@ -434,8 +434,8 @@ class XForwardedForRequest(SynapseRequest):
     """
 
     # the client IP and ssl flag, as extracted from the headers.
-    _forwarded_for = None  # type: Optional[_XForwardedForAddress]
-    _forwarded_https = False  # type: bool
+    _forwarded_for: "Optional[_XForwardedForAddress]" = None
+    _forwarded_https: bool = False
 
     def requestReceived(self, command, path, version):
         # this method is called by the Channel once the full request has been
diff --git a/synapse/logging/_remote.py b/synapse/logging/_remote.py
index c515690b38..8202d0494d 100644
--- a/synapse/logging/_remote.py
+++ b/synapse/logging/_remote.py
@@ -110,9 +110,9 @@ class RemoteHandler(logging.Handler):
         self.port = port
         self.maximum_buffer = maximum_buffer
 
-        self._buffer = deque()  # type: Deque[logging.LogRecord]
-        self._connection_waiter = None  # type: Optional[Deferred]
-        self._producer = None  # type: Optional[LogProducer]
+        self._buffer: Deque[logging.LogRecord] = deque()
+        self._connection_waiter: Optional[Deferred] = None
+        self._producer: Optional[LogProducer] = None
 
         # Connect without DNS lookups if it's a direct IP.
         if _reactor is None:
@@ -123,9 +123,9 @@ class RemoteHandler(logging.Handler):
         try:
             ip = ip_address(self.host)
             if isinstance(ip, IPv4Address):
-                endpoint = TCP4ClientEndpoint(
+                endpoint: IStreamClientEndpoint = TCP4ClientEndpoint(
                     _reactor, self.host, self.port
-                )  # type: IStreamClientEndpoint
+                )
             elif isinstance(ip, IPv6Address):
                 endpoint = TCP6ClientEndpoint(_reactor, self.host, self.port)
             else:
@@ -165,7 +165,7 @@ class RemoteHandler(logging.Handler):
         def writer(result: Protocol) -> None:
             # Force recognising transport as a Connection and not the more
             # generic ITransport.
-            transport = result.transport  # type: Connection  # type: ignore
+            transport: Connection = result.transport  # type: ignore
 
             # We have a connection. If we already have a producer, and its
             # transport is the same, just trigger a resumeProducing.
@@ -188,7 +188,7 @@ class RemoteHandler(logging.Handler):
             self._producer.resumeProducing()
             self._connection_waiter = None
 
-        deferred = self._service.whenConnected(failAfterFailures=1)  # type: Deferred
+        deferred: Deferred = self._service.whenConnected(failAfterFailures=1)
         deferred.addCallbacks(writer, fail)
         self._connection_waiter = deferred
 
diff --git a/synapse/logging/_structured.py b/synapse/logging/_structured.py
index c7a971a9d6..b9933a1528 100644
--- a/synapse/logging/_structured.py
+++ b/synapse/logging/_structured.py
@@ -63,7 +63,7 @@ def parse_drain_configs(
             DrainType.CONSOLE_JSON,
             DrainType.FILE_JSON,
         ):
-            formatter = "json"  # type: Optional[str]
+            formatter: Optional[str] = "json"
         elif logging_type in (
             DrainType.CONSOLE_JSON_TERSE,
             DrainType.NETWORK_JSON_TERSE,
diff --git a/synapse/logging/context.py b/synapse/logging/context.py
index 7fc11a9ac2..18ac507802 100644
--- a/synapse/logging/context.py
+++ b/synapse/logging/context.py
@@ -113,13 +113,13 @@ class ContextResourceUsage:
             self.reset()
         else:
             # FIXME: mypy can't infer the types set via reset() above, so specify explicitly for now
-            self.ru_utime = copy_from.ru_utime  # type: float
-            self.ru_stime = copy_from.ru_stime  # type: float
-            self.db_txn_count = copy_from.db_txn_count  # type: int
+            self.ru_utime: float = copy_from.ru_utime
+            self.ru_stime: float = copy_from.ru_stime
+            self.db_txn_count: int = copy_from.db_txn_count
 
-            self.db_txn_duration_sec = copy_from.db_txn_duration_sec  # type: float
-            self.db_sched_duration_sec = copy_from.db_sched_duration_sec  # type: float
-            self.evt_db_fetch_count = copy_from.evt_db_fetch_count  # type: int
+            self.db_txn_duration_sec: float = copy_from.db_txn_duration_sec
+            self.db_sched_duration_sec: float = copy_from.db_sched_duration_sec
+            self.evt_db_fetch_count: int = copy_from.evt_db_fetch_count
 
     def copy(self) -> "ContextResourceUsage":
         return ContextResourceUsage(copy_from=self)
@@ -289,12 +289,12 @@ class LoggingContext:
 
         # The thread resource usage when the logcontext became active. None
         # if the context is not currently active.
-        self.usage_start = None  # type: Optional[resource._RUsage]
+        self.usage_start: Optional[resource._RUsage] = None
 
         self.main_thread = get_thread_id()
         self.request = None
         self.tag = ""
-        self.scope = None  # type: Optional[_LogContextScope]
+        self.scope: Optional["_LogContextScope"] = None
 
         # keep track of whether we have hit the __exit__ block for this context
         # (suggesting that the the thing that created the context thinks it should
diff --git a/synapse/logging/opentracing.py b/synapse/logging/opentracing.py
index 140ed711e3..185844f188 100644
--- a/synapse/logging/opentracing.py
+++ b/synapse/logging/opentracing.py
@@ -251,7 +251,7 @@ try:
             except Exception:
                 logger.exception("Failed to report span")
 
-    RustReporter = _WrappedRustReporter  # type: Optional[Type[_WrappedRustReporter]]
+    RustReporter: Optional[Type[_WrappedRustReporter]] = _WrappedRustReporter
 except ImportError:
     RustReporter = None
 
@@ -286,7 +286,7 @@ class SynapseBaggage:
 # Block everything by default
 # A regex which matches the server_names to expose traces for.
 # None means 'block everything'.
-_homeserver_whitelist = None  # type: Optional[Pattern[str]]
+_homeserver_whitelist: Optional[Pattern[str]] = None
 
 # Util methods
 
@@ -662,7 +662,7 @@ def inject_header_dict(
 
     span = opentracing.tracer.active_span
 
-    carrier = {}  # type: Dict[str, str]
+    carrier: Dict[str, str] = {}
     opentracing.tracer.inject(span.context, opentracing.Format.HTTP_HEADERS, carrier)
 
     for key, value in carrier.items():
@@ -704,7 +704,7 @@ def get_active_span_text_map(destination=None):
     if destination and not whitelisted_homeserver(destination):
         return {}
 
-    carrier = {}  # type: Dict[str, str]
+    carrier: Dict[str, str] = {}
     opentracing.tracer.inject(
         opentracing.tracer.active_span.context, opentracing.Format.TEXT_MAP, carrier
     )
@@ -718,7 +718,7 @@ def active_span_context_as_string():
     Returns:
         The active span context encoded as a string.
     """
-    carrier = {}  # type: Dict[str, str]
+    carrier: Dict[str, str] = {}
     if opentracing:
         opentracing.tracer.inject(
             opentracing.tracer.active_span.context, opentracing.Format.TEXT_MAP, carrier
diff --git a/synapse/metrics/__init__.py b/synapse/metrics/__init__.py
index fef2846669..f237b8a236 100644
--- a/synapse/metrics/__init__.py
+++ b/synapse/metrics/__init__.py
@@ -46,7 +46,7 @@ logger = logging.getLogger(__name__)
 METRICS_PREFIX = "/_synapse/metrics"
 
 running_on_pypy = platform.python_implementation() == "PyPy"
-all_gauges = {}  # type: Dict[str, Union[LaterGauge, InFlightGauge]]
+all_gauges: "Dict[str, Union[LaterGauge, InFlightGauge]]" = {}
 
 HAVE_PROC_SELF_STAT = os.path.exists("/proc/self/stat")
 
@@ -130,7 +130,7 @@ class InFlightGauge:
         )
 
         # Counts number of in flight blocks for a given set of label values
-        self._registrations = {}  # type: Dict
+        self._registrations: Dict = {}
 
         # Protects access to _registrations
         self._lock = threading.Lock()
@@ -248,7 +248,7 @@ class GaugeBucketCollector:
 
         # We initially set this to None. We won't report metrics until
         # this has been initialised after a successful data update
-        self._metric = None  # type: Optional[GaugeHistogramMetricFamily]
+        self._metric: Optional[GaugeHistogramMetricFamily] = None
 
         registry.register(self)
 
diff --git a/synapse/metrics/_exposition.py b/synapse/metrics/_exposition.py
index 8002be56e0..7e49d0d02c 100644
--- a/synapse/metrics/_exposition.py
+++ b/synapse/metrics/_exposition.py
@@ -125,7 +125,7 @@ def generate_latest(registry, emit_help=False):
             )
         output.append("# TYPE {0} {1}\n".format(mname, mtype))
 
-        om_samples = {}  # type: Dict[str, List[str]]
+        om_samples: Dict[str, List[str]] = {}
         for s in metric.samples:
             for suffix in ["_created", "_gsum", "_gcount"]:
                 if s.name == metric.name + suffix:
diff --git a/synapse/metrics/background_process_metrics.py b/synapse/metrics/background_process_metrics.py
index de96ca0821..4455fa71a8 100644
--- a/synapse/metrics/background_process_metrics.py
+++ b/synapse/metrics/background_process_metrics.py
@@ -93,7 +93,7 @@ _background_process_db_sched_duration = Counter(
 # map from description to a counter, so that we can name our logcontexts
 # incrementally. (It actually duplicates _background_process_start_count, but
 # it's much simpler to do so than to try to combine them.)
-_background_process_counts = {}  # type: Dict[str, int]
+_background_process_counts: Dict[str, int] = {}
 
 # Set of all running background processes that became active active since the
 # last time metrics were scraped (i.e. background processes that performed some
@@ -103,7 +103,7 @@ _background_process_counts = {}  # type: Dict[str, int]
 # background processes stacking up behind a lock or linearizer, where we then
 # only need to iterate over and update metrics for the process that have
 # actually been active and can ignore the idle ones.
-_background_processes_active_since_last_scrape = set()  # type: Set[_BackgroundProcess]
+_background_processes_active_since_last_scrape: "Set[_BackgroundProcess]" = set()
 
 # A lock that covers the above set and dict
 _bg_metrics_lock = threading.Lock()
diff --git a/synapse/module_api/__init__.py b/synapse/module_api/__init__.py
index 721c45abac..308f045700 100644
--- a/synapse/module_api/__init__.py
+++ b/synapse/module_api/__init__.py
@@ -54,7 +54,7 @@ class ModuleApi:
         self._state = hs.get_state_handler()
 
         # We expose these as properties below in order to attach a helpful docstring.
-        self._http_client = hs.get_simple_http_client()  # type: SimpleHttpClient
+        self._http_client: SimpleHttpClient = hs.get_simple_http_client()
         self._public_room_list_manager = PublicRoomListManager(hs)
 
         self._spam_checker = hs.get_spam_checker()
diff --git a/synapse/notifier.py b/synapse/notifier.py
index 3c3cc47631..c5fbebc17d 100644
--- a/synapse/notifier.py
+++ b/synapse/notifier.py
@@ -203,21 +203,21 @@ class Notifier:
     UNUSED_STREAM_EXPIRY_MS = 10 * 60 * 1000
 
     def __init__(self, hs: "synapse.server.HomeServer"):
-        self.user_to_user_stream = {}  # type: Dict[str, _NotifierUserStream]
-        self.room_to_user_streams = {}  # type: Dict[str, Set[_NotifierUserStream]]
+        self.user_to_user_stream: Dict[str, _NotifierUserStream] = {}
+        self.room_to_user_streams: Dict[str, Set[_NotifierUserStream]] = {}
 
         self.hs = hs
         self.storage = hs.get_storage()
         self.event_sources = hs.get_event_sources()
         self.store = hs.get_datastore()
-        self.pending_new_room_events = []  # type: List[_PendingRoomEventEntry]
+        self.pending_new_room_events: List[_PendingRoomEventEntry] = []
 
         # Called when there are new things to stream over replication
-        self.replication_callbacks = []  # type: List[Callable[[], None]]
+        self.replication_callbacks: List[Callable[[], None]] = []
 
         # Called when remote servers have come back online after having been
         # down.
-        self.remote_server_up_callbacks = []  # type: List[Callable[[str], None]]
+        self.remote_server_up_callbacks: List[Callable[[str], None]] = []
 
         self.clock = hs.get_clock()
         self.appservice_handler = hs.get_application_service_handler()
@@ -237,7 +237,7 @@ class Notifier:
         # when rendering the metrics page, which is likely once per minute at
         # most when scraping it.
         def count_listeners():
-            all_user_streams = set()  # type: Set[_NotifierUserStream]
+            all_user_streams: Set[_NotifierUserStream] = set()
 
             for streams in list(self.room_to_user_streams.values()):
                 all_user_streams |= streams
@@ -329,8 +329,8 @@ class Notifier:
         pending = self.pending_new_room_events
         self.pending_new_room_events = []
 
-        users = set()  # type: Set[UserID]
-        rooms = set()  # type: Set[str]
+        users: Set[UserID] = set()
+        rooms: Set[str] = set()
 
         for entry in pending:
             if entry.event_pos.persisted_after(max_room_stream_token):
@@ -580,7 +580,7 @@ class Notifier:
             if after_token == before_token:
                 return EventStreamResult([], (from_token, from_token))
 
-            events = []  # type: List[EventBase]
+            events: List[EventBase] = []
             end_token = from_token
 
             for name, source in self.event_sources.sources.items():
diff --git a/synapse/push/bulk_push_rule_evaluator.py b/synapse/push/bulk_push_rule_evaluator.py
index 669ea462e2..c337e530d3 100644
--- a/synapse/push/bulk_push_rule_evaluator.py
+++ b/synapse/push/bulk_push_rule_evaluator.py
@@ -194,7 +194,7 @@ class BulkPushRuleEvaluator:
         count_as_unread = _should_count_as_unread(event, context)
 
         rules_by_user = await self._get_rules_for_event(event, context)
-        actions_by_user = {}  # type: Dict[str, List[Union[dict, str]]]
+        actions_by_user: Dict[str, List[Union[dict, str]]] = {}
 
         room_members = await self.store.get_joined_users_from_context(event, context)
 
@@ -207,7 +207,7 @@ class BulkPushRuleEvaluator:
             event, len(room_members), sender_power_level, power_levels
         )
 
-        condition_cache = {}  # type: Dict[str, bool]
+        condition_cache: Dict[str, bool] = {}
 
         # If the event is not a state event check if any users ignore the sender.
         if not event.is_state():
diff --git a/synapse/push/clientformat.py b/synapse/push/clientformat.py
index 2ee0ccd58a..1fc9716a34 100644
--- a/synapse/push/clientformat.py
+++ b/synapse/push/clientformat.py
@@ -26,10 +26,10 @@ def format_push_rules_for_user(user: UserID, ruleslist) -> Dict[str, Dict[str, l
     # We're going to be mutating this a lot, so do a deep copy
     ruleslist = copy.deepcopy(ruleslist)
 
-    rules = {
+    rules: Dict[str, Dict[str, List[Dict[str, Any]]]] = {
         "global": {},
         "device": {},
-    }  # type: Dict[str, Dict[str, List[Dict[str, Any]]]]
+    }
 
     rules["global"] = _add_empty_priority_class_arrays(rules["global"])
 
diff --git a/synapse/push/emailpusher.py b/synapse/push/emailpusher.py
index 99a18874d1..e08e125cb8 100644
--- a/synapse/push/emailpusher.py
+++ b/synapse/push/emailpusher.py
@@ -66,8 +66,8 @@ class EmailPusher(Pusher):
 
         self.store = self.hs.get_datastore()
         self.email = pusher_config.pushkey
-        self.timed_call = None  # type: Optional[IDelayedCall]
-        self.throttle_params = {}  # type: Dict[str, ThrottleParams]
+        self.timed_call: Optional[IDelayedCall] = None
+        self.throttle_params: Dict[str, ThrottleParams] = {}
         self._inited = False
 
         self._is_processing = False
@@ -168,7 +168,7 @@ class EmailPusher(Pusher):
             )
         )
 
-        soonest_due_at = None  # type: Optional[int]
+        soonest_due_at: Optional[int] = None
 
         if not unprocessed:
             await self.save_last_stream_ordering_and_success(self.max_stream_ordering)
diff --git a/synapse/push/httppusher.py b/synapse/push/httppusher.py
index 06bf5f8ada..36aabd8422 100644
--- a/synapse/push/httppusher.py
+++ b/synapse/push/httppusher.py
@@ -71,7 +71,7 @@ class HttpPusher(Pusher):
         self.data = pusher_config.data
         self.backoff_delay = HttpPusher.INITIAL_BACKOFF_SEC
         self.failing_since = pusher_config.failing_since
-        self.timed_call = None  # type: Optional[IDelayedCall]
+        self.timed_call: Optional[IDelayedCall] = None
         self._is_processing = False
         self._group_unread_count_by_room = hs.config.push_group_unread_count_by_room
         self._pusherpool = hs.get_pusherpool()
diff --git a/synapse/push/mailer.py b/synapse/push/mailer.py
index 5f9ea5003a..7be5fe1e9b 100644
--- a/synapse/push/mailer.py
+++ b/synapse/push/mailer.py
@@ -110,7 +110,7 @@ class Mailer:
         self.state_handler = self.hs.get_state_handler()
         self.storage = hs.get_storage()
         self.app_name = app_name
-        self.email_subjects = hs.config.email_subjects  # type: EmailSubjectConfig
+        self.email_subjects: EmailSubjectConfig = hs.config.email_subjects
 
         logger.info("Created Mailer for app_name %s" % app_name)
 
@@ -230,7 +230,7 @@ class Mailer:
             [pa["event_id"] for pa in push_actions]
         )
 
-        notifs_by_room = {}  # type: Dict[str, List[Dict[str, Any]]]
+        notifs_by_room: Dict[str, List[Dict[str, Any]]] = {}
         for pa in push_actions:
             notifs_by_room.setdefault(pa["room_id"], []).append(pa)
 
@@ -356,13 +356,13 @@ class Mailer:
 
         room_name = await calculate_room_name(self.store, room_state_ids, user_id)
 
-        room_vars = {
+        room_vars: Dict[str, Any] = {
             "title": room_name,
             "hash": string_ordinal_total(room_id),  # See sender avatar hash
             "notifs": [],
             "invite": is_invite,
             "link": self._make_room_link(room_id),
-        }  # type: Dict[str, Any]
+        }
 
         if not is_invite:
             for n in notifs:
@@ -460,9 +460,9 @@ class Mailer:
         type_state_key = ("m.room.member", event.sender)
         sender_state_event_id = room_state_ids.get(type_state_key)
         if sender_state_event_id:
-            sender_state_event = await self.store.get_event(
+            sender_state_event: Optional[EventBase] = await self.store.get_event(
                 sender_state_event_id
-            )  # type: Optional[EventBase]
+            )
         else:
             # Attempt to check the historical state for the room.
             historical_state = await self.state_store.get_state_for_event(
diff --git a/synapse/push/presentable_names.py b/synapse/push/presentable_names.py
index 412941393f..0510c1cbd5 100644
--- a/synapse/push/presentable_names.py
+++ b/synapse/push/presentable_names.py
@@ -199,7 +199,7 @@ def name_from_member_event(member_event: EventBase) -> str:
 
 
 def _state_as_two_level_dict(state: StateMap[str]) -> Dict[str, Dict[str, str]]:
-    ret = {}  # type: Dict[str, Dict[str, str]]
+    ret: Dict[str, Dict[str, str]] = {}
     for k, v in state.items():
         ret.setdefault(k[0], {})[k[1]] = v
     return ret
diff --git a/synapse/push/push_rule_evaluator.py b/synapse/push/push_rule_evaluator.py
index 98b90a4f51..7a8dc63976 100644
--- a/synapse/push/push_rule_evaluator.py
+++ b/synapse/push/push_rule_evaluator.py
@@ -195,9 +195,9 @@ class PushRuleEvaluatorForEvent:
 
 
 # Caches (string, is_glob, word_boundary) -> regex for push. See _glob_matches
-regex_cache = LruCache(
+regex_cache: LruCache[Tuple[str, bool, bool], Pattern] = LruCache(
     50000, "regex_push_cache"
-)  # type: LruCache[Tuple[str, bool, bool], Pattern]
+)
 
 
 def _glob_matches(glob: str, value: str, word_boundary: bool = False) -> bool:
diff --git a/synapse/push/pusher.py b/synapse/push/pusher.py
index c51938b8cf..021275437c 100644
--- a/synapse/push/pusher.py
+++ b/synapse/push/pusher.py
@@ -31,13 +31,13 @@ class PusherFactory:
         self.hs = hs
         self.config = hs.config
 
-        self.pusher_types = {
+        self.pusher_types: Dict[str, Callable[[HomeServer, PusherConfig], Pusher]] = {
             "http": HttpPusher
-        }  # type: Dict[str, Callable[[HomeServer, PusherConfig], Pusher]]
+        }
 
         logger.info("email enable notifs: %r", hs.config.email_enable_notifs)
         if hs.config.email_enable_notifs:
-            self.mailers = {}  # type: Dict[str, Mailer]
+            self.mailers: Dict[str, Mailer] = {}
 
             self._notif_template_html = hs.config.email_notif_template_html
             self._notif_template_text = hs.config.email_notif_template_text
diff --git a/synapse/push/pusherpool.py b/synapse/push/pusherpool.py
index 579fcdf472..2519ad76db 100644
--- a/synapse/push/pusherpool.py
+++ b/synapse/push/pusherpool.py
@@ -87,7 +87,7 @@ class PusherPool:
         self._last_room_stream_id_seen = self.store.get_room_max_stream_ordering()
 
         # map from user id to app_id:pushkey to pusher
-        self.pushers = {}  # type: Dict[str, Dict[str, Pusher]]
+        self.pushers: Dict[str, Dict[str, Pusher]] = {}
 
     def start(self) -> None:
         """Starts the pushers off in a background process."""
diff --git a/synapse/python_dependencies.py b/synapse/python_dependencies.py
index 271c17c226..cdcbdd772b 100644
--- a/synapse/python_dependencies.py
+++ b/synapse/python_dependencies.py
@@ -115,7 +115,7 @@ CONDITIONAL_REQUIREMENTS = {
     "cache_memory": ["pympler"],
 }
 
-ALL_OPTIONAL_REQUIREMENTS = set()  # type: Set[str]
+ALL_OPTIONAL_REQUIREMENTS: Set[str] = set()
 
 for name, optional_deps in CONDITIONAL_REQUIREMENTS.items():
     # Exclude systemd as it's a system-based requirement.
@@ -193,7 +193,7 @@ def check_requirements(for_feature=None):
     if not for_feature:
         # Check the optional dependencies are up to date. We allow them to not be
         # installed.
-        OPTS = sum(CONDITIONAL_REQUIREMENTS.values(), [])  # type: List[str]
+        OPTS: List[str] = sum(CONDITIONAL_REQUIREMENTS.values(), [])
 
         for dependency in OPTS:
             try:
diff --git a/synapse/replication/http/_base.py b/synapse/replication/http/_base.py
index f13a7c23b4..25589b0042 100644
--- a/synapse/replication/http/_base.py
+++ b/synapse/replication/http/_base.py
@@ -85,17 +85,17 @@ class ReplicationEndpoint(metaclass=abc.ABCMeta):
             is received.
     """
 
-    NAME = abc.abstractproperty()  # type: str  # type: ignore
-    PATH_ARGS = abc.abstractproperty()  # type: Tuple[str, ...]  # type: ignore
+    NAME: str = abc.abstractproperty()  # type: ignore
+    PATH_ARGS: Tuple[str, ...] = abc.abstractproperty()  # type: ignore
     METHOD = "POST"
     CACHE = True
     RETRY_ON_TIMEOUT = True
 
     def __init__(self, hs: "HomeServer"):
         if self.CACHE:
-            self.response_cache = ResponseCache(
+            self.response_cache: ResponseCache[str] = ResponseCache(
                 hs.get_clock(), "repl." + self.NAME, timeout_ms=30 * 60 * 1000
-            )  # type: ResponseCache[str]
+            )
 
         # We reserve `instance_name` as a parameter to sending requests, so we
         # assert here that sub classes don't try and use the name.
@@ -232,7 +232,7 @@ class ReplicationEndpoint(metaclass=abc.ABCMeta):
                 # have a good idea that the request has either succeeded or failed on
                 # the master, and so whether we should clean up or not.
                 while True:
-                    headers = {}  # type: Dict[bytes, List[bytes]]
+                    headers: Dict[bytes, List[bytes]] = {}
                     # Add an authorization header, if configured.
                     if replication_secret:
                         headers[b"Authorization"] = [b"Bearer " + replication_secret]
diff --git a/synapse/replication/slave/storage/_base.py b/synapse/replication/slave/storage/_base.py
index faa99387a7..e460dd85cd 100644
--- a/synapse/replication/slave/storage/_base.py
+++ b/synapse/replication/slave/storage/_base.py
@@ -27,7 +27,9 @@ class BaseSlavedStore(CacheInvalidationWorkerStore):
     def __init__(self, database: DatabasePool, db_conn, hs):
         super().__init__(database, db_conn, hs)
         if isinstance(self.database_engine, PostgresEngine):
-            self._cache_id_gen = MultiWriterIdGenerator(
+            self._cache_id_gen: Optional[
+                MultiWriterIdGenerator
+            ] = MultiWriterIdGenerator(
                 db_conn,
                 database,
                 stream_name="caches",
@@ -41,7 +43,7 @@ class BaseSlavedStore(CacheInvalidationWorkerStore):
                 ],
                 sequence_name="cache_invalidation_stream_seq",
                 writers=[],
-            )  # type: Optional[MultiWriterIdGenerator]
+            )
         else:
             self._cache_id_gen = None
 
diff --git a/synapse/replication/slave/storage/client_ips.py b/synapse/replication/slave/storage/client_ips.py
index 13ed87adc4..436d39c320 100644
--- a/synapse/replication/slave/storage/client_ips.py
+++ b/synapse/replication/slave/storage/client_ips.py
@@ -23,9 +23,9 @@ class SlavedClientIpStore(BaseSlavedStore):
     def __init__(self, database: DatabasePool, db_conn, hs):
         super().__init__(database, db_conn, hs)
 
-        self.client_ip_last_seen = LruCache(
+        self.client_ip_last_seen: LruCache[tuple, int] = LruCache(
             cache_name="client_ip_last_seen", max_size=50000
-        )  # type: LruCache[tuple, int]
+        )
 
     async def insert_client_ip(self, user_id, access_token, ip, user_agent, device_id):
         now = int(self._clock.time_msec())
diff --git a/synapse/replication/tcp/client.py b/synapse/replication/tcp/client.py
index 62d7809175..9d4859798b 100644
--- a/synapse/replication/tcp/client.py
+++ b/synapse/replication/tcp/client.py
@@ -121,13 +121,13 @@ class ReplicationDataHandler:
         self._pusher_pool = hs.get_pusherpool()
         self._presence_handler = hs.get_presence_handler()
 
-        self.send_handler = None  # type: Optional[FederationSenderHandler]
+        self.send_handler: Optional[FederationSenderHandler] = None
         if hs.should_send_federation():
             self.send_handler = FederationSenderHandler(hs)
 
         # Map from stream to list of deferreds waiting for the stream to
         # arrive at a particular position. The lists are sorted by stream position.
-        self._streams_to_waiters = {}  # type: Dict[str, List[Tuple[int, Deferred]]]
+        self._streams_to_waiters: Dict[str, List[Tuple[int, Deferred]]] = {}
 
     async def on_rdata(
         self, stream_name: str, instance_name: str, token: int, rows: list
@@ -173,7 +173,7 @@ class ReplicationDataHandler:
             if entities:
                 self.notifier.on_new_event("to_device_key", token, users=entities)
         elif stream_name == DeviceListsStream.NAME:
-            all_room_ids = set()  # type: Set[str]
+            all_room_ids: Set[str] = set()
             for row in rows:
                 if row.entity.startswith("@"):
                     room_ids = await self.store.get_rooms_for_user(row.entity)
@@ -201,7 +201,7 @@ class ReplicationDataHandler:
                 if row.data.rejected:
                     continue
 
-                extra_users = ()  # type: Tuple[UserID, ...]
+                extra_users: Tuple[UserID, ...] = ()
                 if row.data.type == EventTypes.Member and row.data.state_key:
                     extra_users = (UserID.from_string(row.data.state_key),)
 
@@ -348,7 +348,7 @@ class FederationSenderHandler:
 
         # Stores the latest position in the federation stream we've gotten up
         # to. This is always set before we use it.
-        self.federation_position = None  # type: Optional[int]
+        self.federation_position: Optional[int] = None
 
         self._fed_position_linearizer = Linearizer(name="_fed_position_linearizer")
 
diff --git a/synapse/replication/tcp/commands.py b/synapse/replication/tcp/commands.py
index 505d450e19..1311b013da 100644
--- a/synapse/replication/tcp/commands.py
+++ b/synapse/replication/tcp/commands.py
@@ -34,7 +34,7 @@ class Command(metaclass=abc.ABCMeta):
     A full command line on the wire is constructed from `NAME + " " + to_line()`
     """
 
-    NAME = None  # type: str
+    NAME: str
 
     @classmethod
     @abc.abstractmethod
@@ -380,7 +380,7 @@ class RemoteServerUpCommand(_SimpleCommand):
     NAME = "REMOTE_SERVER_UP"
 
 
-_COMMANDS = (
+_COMMANDS: Tuple[Type[Command], ...] = (
     ServerCommand,
     RdataCommand,
     PositionCommand,
@@ -393,7 +393,7 @@ _COMMANDS = (
     UserIpCommand,
     RemoteServerUpCommand,
     ClearUserSyncsCommand,
-)  # type: Tuple[Type[Command], ...]
+)
 
 # Map of command name to command type.
 COMMAND_MAP = {cmd.NAME: cmd for cmd in _COMMANDS}
diff --git a/synapse/replication/tcp/handler.py b/synapse/replication/tcp/handler.py
index 2ad7a200bb..eae4515363 100644
--- a/synapse/replication/tcp/handler.py
+++ b/synapse/replication/tcp/handler.py
@@ -105,12 +105,12 @@ class ReplicationCommandHandler:
             hs.get_instance_name() in hs.config.worker.writers.presence
         )
 
-        self._streams = {
+        self._streams: Dict[str, Stream] = {
             stream.NAME: stream(hs) for stream in STREAMS_MAP.values()
-        }  # type: Dict[str, Stream]
+        }
 
         # List of streams that this instance is the source of
-        self._streams_to_replicate = []  # type: List[Stream]
+        self._streams_to_replicate: List[Stream] = []
 
         for stream in self._streams.values():
             if hs.config.redis.redis_enabled and stream.NAME == CachesStream.NAME:
@@ -180,14 +180,14 @@ class ReplicationCommandHandler:
 
         # Map of stream name to batched updates. See RdataCommand for info on
         # how batching works.
-        self._pending_batches = {}  # type: Dict[str, List[Any]]
+        self._pending_batches: Dict[str, List[Any]] = {}
 
         # The factory used to create connections.
-        self._factory = None  # type: Optional[ReconnectingClientFactory]
+        self._factory: Optional[ReconnectingClientFactory] = None
 
         # The currently connected connections. (The list of places we need to send
         # outgoing replication commands to.)
-        self._connections = []  # type: List[IReplicationConnection]
+        self._connections: List[IReplicationConnection] = []
 
         LaterGauge(
             "synapse_replication_tcp_resource_total_connections",
@@ -200,7 +200,7 @@ class ReplicationCommandHandler:
         # them in order in a separate background process.
 
         # the streams which are currently being processed by _unsafe_process_queue
-        self._processing_streams = set()  # type: Set[str]
+        self._processing_streams: Set[str] = set()
 
         # for each stream, a queue of commands that are awaiting processing, and the
         # connection that they arrived on.
@@ -210,7 +210,7 @@ class ReplicationCommandHandler:
 
         # For each connection, the incoming stream names that have received a POSITION
         # from that connection.
-        self._streams_by_connection = {}  # type: Dict[IReplicationConnection, Set[str]]
+        self._streams_by_connection: Dict[IReplicationConnection, Set[str]] = {}
 
         LaterGauge(
             "synapse_replication_tcp_command_queue",
diff --git a/synapse/replication/tcp/protocol.py b/synapse/replication/tcp/protocol.py
index 6e3705364f..8c80153ab6 100644
--- a/synapse/replication/tcp/protocol.py
+++ b/synapse/replication/tcp/protocol.py
@@ -102,7 +102,7 @@ tcp_outbound_commands_counter = Counter(
 
 # A list of all connected protocols. This allows us to send metrics about the
 # connections.
-connected_connections = []  # type: List[BaseReplicationStreamProtocol]
+connected_connections: "List[BaseReplicationStreamProtocol]" = []
 
 
 logger = logging.getLogger(__name__)
@@ -146,15 +146,15 @@ class BaseReplicationStreamProtocol(LineOnlyReceiver):
 
     # The transport is going to be an ITCPTransport, but that doesn't have the
     # (un)registerProducer methods, those are only on the implementation.
-    transport = None  # type: Connection
+    transport: Connection
 
     delimiter = b"\n"
 
     # Valid commands we expect to receive
-    VALID_INBOUND_COMMANDS = []  # type: Collection[str]
+    VALID_INBOUND_COMMANDS: Collection[str] = []
 
     # Valid commands we can send
-    VALID_OUTBOUND_COMMANDS = []  # type: Collection[str]
+    VALID_OUTBOUND_COMMANDS: Collection[str] = []
 
     max_line_buffer = 10000
 
@@ -165,7 +165,7 @@ class BaseReplicationStreamProtocol(LineOnlyReceiver):
         self.last_received_command = self.clock.time_msec()
         self.last_sent_command = 0
         # When we requested the connection be closed
-        self.time_we_closed = None  # type: Optional[int]
+        self.time_we_closed: Optional[int] = None
 
         self.received_ping = False  # Have we received a ping from the other side
 
@@ -175,10 +175,10 @@ class BaseReplicationStreamProtocol(LineOnlyReceiver):
         self.conn_id = random_string(5)  # To dedupe in case of name clashes.
 
         # List of pending commands to send once we've established the connection
-        self.pending_commands = []  # type: List[Command]
+        self.pending_commands: List[Command] = []
 
         # The LoopingCall for sending pings.
-        self._send_ping_loop = None  # type: Optional[task.LoopingCall]
+        self._send_ping_loop: Optional[task.LoopingCall] = None
 
         # a logcontext which we use for processing incoming commands. We declare it as a
         # background process so that the CPU stats get reported to prometheus.
diff --git a/synapse/replication/tcp/redis.py b/synapse/replication/tcp/redis.py
index 6a2c2655e4..8c0df627c8 100644
--- a/synapse/replication/tcp/redis.py
+++ b/synapse/replication/tcp/redis.py
@@ -57,7 +57,7 @@ class ConstantProperty(Generic[T, V]):
     it.
     """
 
-    constant = attr.ib()  # type: V
+    constant: V = attr.ib()
 
     def __get__(self, obj: Optional[T], objtype: Optional[Type[T]] = None) -> V:
         return self.constant
@@ -91,9 +91,9 @@ class RedisSubscriber(txredisapi.SubscriberProtocol):
             commands.
     """
 
-    synapse_handler = None  # type: ReplicationCommandHandler
-    synapse_stream_name = None  # type: str
-    synapse_outbound_redis_connection = None  # type: txredisapi.RedisProtocol
+    synapse_handler: "ReplicationCommandHandler"
+    synapse_stream_name: str
+    synapse_outbound_redis_connection: txredisapi.RedisProtocol
 
     def __init__(self, *args, **kwargs):
         super().__init__(*args, **kwargs)
diff --git a/synapse/replication/tcp/streams/_base.py b/synapse/replication/tcp/streams/_base.py
index b03824925a..3716c41bea 100644
--- a/synapse/replication/tcp/streams/_base.py
+++ b/synapse/replication/tcp/streams/_base.py
@@ -85,9 +85,9 @@ class Stream:
     time it was called.
     """
 
-    NAME = None  # type: str  # The name of the stream
+    NAME: str  # The name of the stream
     # The type of the row. Used by the default impl of parse_row.
-    ROW_TYPE = None  # type: Any
+    ROW_TYPE: Any = None
 
     @classmethod
     def parse_row(cls, row: StreamRow):
@@ -283,9 +283,7 @@ class PresenceStream(Stream):
 
             assert isinstance(presence_handler, PresenceHandler)
 
-            update_function = (
-                presence_handler.get_all_presence_updates
-            )  # type: UpdateFunction
+            update_function: UpdateFunction = presence_handler.get_all_presence_updates
         else:
             # Query presence writer process
             update_function = make_http_update_function(hs, self.NAME)
@@ -334,9 +332,9 @@ class TypingStream(Stream):
         if writer_instance == hs.get_instance_name():
             # On the writer, query the typing handler
             typing_writer_handler = hs.get_typing_writer_handler()
-            update_function = (
-                typing_writer_handler.get_all_typing_updates
-            )  # type: Callable[[str, int, int, int], Awaitable[Tuple[List[Tuple[int, Any]], int, bool]]]
+            update_function: Callable[
+                [str, int, int, int], Awaitable[Tuple[List[Tuple[int, Any]], int, bool]]
+            ] = typing_writer_handler.get_all_typing_updates
             current_token_function = typing_writer_handler.get_current_token
         else:
             # Query the typing writer process
diff --git a/synapse/replication/tcp/streams/events.py b/synapse/replication/tcp/streams/events.py
index e7e87bac92..a030e9299e 100644
--- a/synapse/replication/tcp/streams/events.py
+++ b/synapse/replication/tcp/streams/events.py
@@ -65,7 +65,7 @@ class BaseEventsStreamRow:
     """
 
     # Unique string that ids the type. Must be overridden in sub classes.
-    TypeId = None  # type: str
+    TypeId: str
 
     @classmethod
     def from_data(cls, data):
@@ -103,10 +103,10 @@ class EventsStreamCurrentStateRow(BaseEventsStreamRow):
     event_id = attr.ib()  # str, optional
 
 
-_EventRows = (
+_EventRows: Tuple[Type[BaseEventsStreamRow], ...] = (
     EventsStreamEventRow,
     EventsStreamCurrentStateRow,
-)  # type: Tuple[Type[BaseEventsStreamRow], ...]
+)
 
 TypeToRow = {Row.TypeId: Row for Row in _EventRows}
 
@@ -157,9 +157,9 @@ class EventsStream(Stream):
 
         # now we fetch up to that many rows from the events table
 
-        event_rows = await self._store.get_all_new_forward_event_rows(
+        event_rows: List[Tuple] = await self._store.get_all_new_forward_event_rows(
             instance_name, from_token, current_token, target_row_count
-        )  # type: List[Tuple]
+        )
 
         # we rely on get_all_new_forward_event_rows strictly honouring the limit, so
         # that we know it is safe to just take upper_limit = event_rows[-1][0].
@@ -172,7 +172,7 @@ class EventsStream(Stream):
 
         if len(event_rows) == target_row_count:
             limited = True
-            upper_limit = event_rows[-1][0]  # type: int
+            upper_limit: int = event_rows[-1][0]
         else:
             limited = False
             upper_limit = current_token
@@ -191,30 +191,30 @@ class EventsStream(Stream):
         # finally, fetch the ex-outliers rows. We assume there are few enough of these
         # not to bother with the limit.
 
-        ex_outliers_rows = await self._store.get_ex_outlier_stream_rows(
+        ex_outliers_rows: List[Tuple] = await self._store.get_ex_outlier_stream_rows(
             instance_name, from_token, upper_limit
-        )  # type: List[Tuple]
+        )
 
         # we now need to turn the raw database rows returned into tuples suitable
         # for the replication protocol (basically, we add an identifier to
         # distinguish the row type). At the same time, we can limit the event_rows
         # to the max stream_id from state_rows.
 
-        event_updates = (
+        event_updates: Iterable[Tuple[int, Tuple]] = (
             (stream_id, (EventsStreamEventRow.TypeId, rest))
             for (stream_id, *rest) in event_rows
             if stream_id <= upper_limit
-        )  # type: Iterable[Tuple[int, Tuple]]
+        )
 
-        state_updates = (
+        state_updates: Iterable[Tuple[int, Tuple]] = (
             (stream_id, (EventsStreamCurrentStateRow.TypeId, rest))
             for (stream_id, *rest) in state_rows
-        )  # type: Iterable[Tuple[int, Tuple]]
+        )
 
-        ex_outliers_updates = (
+        ex_outliers_updates: Iterable[Tuple[int, Tuple]] = (
             (stream_id, (EventsStreamEventRow.TypeId, rest))
             for (stream_id, *rest) in ex_outliers_rows
-        )  # type: Iterable[Tuple[int, Tuple]]
+        )
 
         # we need to return a sorted list, so merge them together.
         updates = list(heapq.merge(event_updates, state_updates, ex_outliers_updates))
diff --git a/synapse/replication/tcp/streams/federation.py b/synapse/replication/tcp/streams/federation.py
index 096a85d363..c445af9bd9 100644
--- a/synapse/replication/tcp/streams/federation.py
+++ b/synapse/replication/tcp/streams/federation.py
@@ -51,9 +51,9 @@ class FederationStream(Stream):
             current_token = current_token_without_instance(
                 federation_sender.get_current_token
             )
-            update_function = (
-                federation_sender.get_replication_rows
-            )  # type: Callable[[str, int, int, int], Awaitable[Tuple[List[Tuple[int, Any]], int, bool]]]
+            update_function: Callable[
+                [str, int, int, int], Awaitable[Tuple[List[Tuple[int, Any]], int, bool]]
+            ] = federation_sender.get_replication_rows
 
         elif hs.should_send_federation():
             # federation sender: Query master process
diff --git a/synapse/rest/admin/rooms.py b/synapse/rest/admin/rooms.py
index f0cddd2d2c..3c51a742bf 100644
--- a/synapse/rest/admin/rooms.py
+++ b/synapse/rest/admin/rooms.py
@@ -462,6 +462,7 @@ class MakeRoomAdminRestServlet(ResolveRoomIdMixin, RestServlet):
         super().__init__(hs)
         self.hs = hs
         self.auth = hs.get_auth()
+        self.store = hs.get_datastore()
         self.event_creation_handler = hs.get_event_creation_handler()
         self.state_handler = hs.get_state_handler()
         self.is_mine_id = hs.is_mine_id
@@ -500,7 +501,13 @@ class MakeRoomAdminRestServlet(ResolveRoomIdMixin, RestServlet):
             admin_user_id = None
 
             for admin_user in reversed(admin_users):
-                if room_state.get((EventTypes.Member, admin_user)):
+                (
+                    current_membership_type,
+                    _,
+                ) = await self.store.get_local_current_membership_for_user_in_room(
+                    admin_user, room_id
+                )
+                if current_membership_type == "join":
                     admin_user_id = admin_user
                     break
 
diff --git a/synapse/rest/client/v1/room.py b/synapse/rest/client/v1/room.py
index 92ebe838fd..ebf4e32230 100644
--- a/synapse/rest/client/v1/room.py
+++ b/synapse/rest/client/v1/room.py
@@ -29,6 +29,7 @@ from synapse.api.errors import (
     SynapseError,
 )
 from synapse.api.filtering import Filter
+from synapse.appservice import ApplicationService
 from synapse.events.utils import format_event_for_client_v2
 from synapse.http.servlet import (
     RestServlet,
@@ -47,11 +48,13 @@ from synapse.storage.state import StateFilter
 from synapse.streams.config import PaginationConfig
 from synapse.types import (
     JsonDict,
+    Requester,
     RoomAlias,
     RoomID,
     StreamToken,
     ThirdPartyInstanceID,
     UserID,
+    create_requester,
 )
 from synapse.util import json_decoder
 from synapse.util.stringutils import parse_and_validate_server_name, random_string
@@ -309,7 +312,7 @@ class RoomBatchSendEventRestServlet(TransactionRestServlet):
         self.room_member_handler = hs.get_room_member_handler()
         self.auth = hs.get_auth()
 
-    async def inherit_depth_from_prev_ids(self, prev_event_ids) -> int:
+    async def _inherit_depth_from_prev_ids(self, prev_event_ids) -> int:
         (
             most_recent_prev_event_id,
             most_recent_prev_event_depth,
@@ -349,6 +352,54 @@ class RoomBatchSendEventRestServlet(TransactionRestServlet):
 
         return depth
 
+    def _create_insertion_event_dict(
+        self, sender: str, room_id: str, origin_server_ts: int
+    ):
+        """Creates an event dict for an "insertion" event with the proper fields
+        and a random chunk ID.
+
+        Args:
+            sender: The event author MXID
+            room_id: The room ID that the event belongs to
+            origin_server_ts: Timestamp when the event was sent
+
+        Returns:
+            Tuple of event ID and stream ordering position
+        """
+
+        next_chunk_id = random_string(8)
+        insertion_event = {
+            "type": EventTypes.MSC2716_INSERTION,
+            "sender": sender,
+            "room_id": room_id,
+            "content": {
+                EventContentFields.MSC2716_NEXT_CHUNK_ID: next_chunk_id,
+                EventContentFields.MSC2716_HISTORICAL: True,
+            },
+            "origin_server_ts": origin_server_ts,
+        }
+
+        return insertion_event
+
+    async def _create_requester_for_user_id_from_app_service(
+        self, user_id: str, app_service: ApplicationService
+    ) -> Requester:
+        """Creates a new requester for the given user_id
+        and validates that the app service is allowed to control
+        the given user.
+
+        Args:
+            user_id: The author MXID that the app service is controlling
+            app_service: The app service that controls the user
+
+        Returns:
+            Requester object
+        """
+
+        await self.auth.validate_appservice_can_control_user_id(app_service, user_id)
+
+        return create_requester(user_id, app_service=app_service)
+
     async def on_POST(self, request, room_id):
         requester = await self.auth.get_user_by_req(request, allow_guest=False)
 
@@ -414,7 +465,9 @@ class RoomBatchSendEventRestServlet(TransactionRestServlet):
             if event_dict["type"] == EventTypes.Member:
                 membership = event_dict["content"].get("membership", None)
                 event_id, _ = await self.room_member_handler.update_membership(
-                    requester,
+                    await self._create_requester_for_user_id_from_app_service(
+                        state_event["sender"], requester.app_service
+                    ),
                     target=UserID.from_string(event_dict["state_key"]),
                     room_id=room_id,
                     action=membership,
@@ -434,7 +487,9 @@ class RoomBatchSendEventRestServlet(TransactionRestServlet):
                     event,
                     _,
                 ) = await self.event_creation_handler.create_and_send_nonmember_event(
-                    requester,
+                    await self._create_requester_for_user_id_from_app_service(
+                        state_event["sender"], requester.app_service
+                    ),
                     event_dict,
                     outlier=True,
                     prev_event_ids=[fake_prev_event_id],
@@ -449,37 +504,73 @@ class RoomBatchSendEventRestServlet(TransactionRestServlet):
 
         events_to_create = body["events"]
 
-        # If provided, connect the chunk to the last insertion point
-        # The chunk ID passed in comes from the chunk_id in the
-        # "insertion" event from the previous chunk.
+        prev_event_ids = prev_events_from_query
+        inherited_depth = await self._inherit_depth_from_prev_ids(
+            prev_events_from_query
+        )
+
+        # Figure out which chunk to connect to. If they passed in
+        # chunk_id_from_query let's use it. The chunk ID passed in comes
+        # from the chunk_id in the "insertion" event from the previous chunk.
+        last_event_in_chunk = events_to_create[-1]
+        chunk_id_to_connect_to = chunk_id_from_query
+        base_insertion_event = None
         if chunk_id_from_query:
-            last_event_in_chunk = events_to_create[-1]
-            last_event_in_chunk["content"][
-                EventContentFields.MSC2716_CHUNK_ID
-            ] = chunk_id_from_query
+            # TODO: Verify the chunk_id_from_query corresponds to an insertion event
+            pass
+        # Otherwise, create an insertion event to act as a starting point.
+        #
+        # We don't always have an insertion event to start hanging more history
+        # off of (ideally there would be one in the main DAG, but that's not the
+        # case if we're wanting to add history to e.g. existing rooms without
+        # an insertion event), in which case we just create a new insertion event
+        # that can then get pointed to by a "marker" event later.
+        else:
+            base_insertion_event_dict = self._create_insertion_event_dict(
+                sender=requester.user.to_string(),
+                room_id=room_id,
+                origin_server_ts=last_event_in_chunk["origin_server_ts"],
+            )
+            base_insertion_event_dict["prev_events"] = prev_event_ids.copy()
+
+            (
+                base_insertion_event,
+                _,
+            ) = await self.event_creation_handler.create_and_send_nonmember_event(
+                await self._create_requester_for_user_id_from_app_service(
+                    base_insertion_event_dict["sender"],
+                    requester.app_service,
+                ),
+                base_insertion_event_dict,
+                prev_event_ids=base_insertion_event_dict.get("prev_events"),
+                auth_event_ids=auth_event_ids,
+                historical=True,
+                depth=inherited_depth,
+            )
+
+            chunk_id_to_connect_to = base_insertion_event["content"][
+                EventContentFields.MSC2716_NEXT_CHUNK_ID
+            ]
 
-        # Add an "insertion" event to the start of each chunk (next to the oldest
+        # Connect this current chunk to the insertion event from the previous chunk
+        last_event_in_chunk["content"][
+            EventContentFields.MSC2716_CHUNK_ID
+        ] = chunk_id_to_connect_to
+
+        # Add an "insertion" event to the start of each chunk (next to the oldest-in-time
         # event in the chunk) so the next chunk can be connected to this one.
-        next_chunk_id = random_string(64)
-        insertion_event = {
-            "type": EventTypes.MSC2716_INSERTION,
-            "sender": requester.user.to_string(),
-            "content": {
-                EventContentFields.MSC2716_NEXT_CHUNK_ID: next_chunk_id,
-                EventContentFields.MSC2716_HISTORICAL: True,
-            },
+        insertion_event = self._create_insertion_event_dict(
+            sender=requester.user.to_string(),
+            room_id=room_id,
             # Since the insertion event is put at the start of the chunk,
-            # where the oldest event is, copy the origin_server_ts from
+            # where the oldest-in-time event is, copy the origin_server_ts from
             # the first event we're inserting
-            "origin_server_ts": events_to_create[0]["origin_server_ts"],
-        }
+            origin_server_ts=events_to_create[0]["origin_server_ts"],
+        )
         # Prepend the insertion event to the start of the chunk
         events_to_create = [insertion_event] + events_to_create
 
-        inherited_depth = await self.inherit_depth_from_prev_ids(prev_events_from_query)
-
         event_ids = []
-        prev_event_ids = prev_events_from_query
         events_to_persist = []
         for ev in events_to_create:
             assert_params_in_dict(ev, ["type", "origin_server_ts", "content", "sender"])
@@ -498,7 +589,9 @@ class RoomBatchSendEventRestServlet(TransactionRestServlet):
             }
 
             event, context = await self.event_creation_handler.create_event(
-                requester,
+                await self._create_requester_for_user_id_from_app_service(
+                    ev["sender"], requester.app_service
+                ),
                 event_dict,
                 prev_event_ids=event_dict.get("prev_events"),
                 auth_event_ids=auth_event_ids,
@@ -528,15 +621,23 @@ class RoomBatchSendEventRestServlet(TransactionRestServlet):
         # where topological_ordering is just depth.
         for (event, context) in reversed(events_to_persist):
             ev = await self.event_creation_handler.handle_new_client_event(
-                requester=requester,
+                await self._create_requester_for_user_id_from_app_service(
+                    event["sender"], requester.app_service
+                ),
                 event=event,
                 context=context,
             )
 
+        # Add the base_insertion_event to the bottom of the list we return
+        if base_insertion_event is not None:
+            event_ids.append(base_insertion_event.event_id)
+
         return 200, {
             "state_events": auth_event_ids,
             "events": event_ids,
-            "next_chunk_id": next_chunk_id,
+            "next_chunk_id": insertion_event["content"][
+                EventContentFields.MSC2716_NEXT_CHUNK_ID
+            ],
         }
 
     def on_GET(self, request, room_id):
diff --git a/synapse/server.py b/synapse/server.py
index 2c27d2a7e8..095dba9ad0 100644
--- a/synapse/server.py
+++ b/synapse/server.py
@@ -247,15 +247,15 @@ class HomeServer(metaclass=abc.ABCMeta):
         # the key we use to sign events and requests
         self.signing_key = config.key.signing_key[0]
         self.config = config
-        self._listening_services = []  # type: List[twisted.internet.tcp.Port]
-        self.start_time = None  # type: Optional[int]
+        self._listening_services: List[twisted.internet.tcp.Port] = []
+        self.start_time: Optional[int] = None
 
         self._instance_id = random_string(5)
         self._instance_name = config.worker.instance_name
 
         self.version_string = version_string
 
-        self.datastores = None  # type: Optional[Databases]
+        self.datastores: Optional[Databases] = None
 
         self._module_web_resources: Dict[str, IResource] = {}
         self._module_web_resources_consumed = False
diff --git a/synapse/server_notices/consent_server_notices.py b/synapse/server_notices/consent_server_notices.py
index e65f6f88fe..4e0f814035 100644
--- a/synapse/server_notices/consent_server_notices.py
+++ b/synapse/server_notices/consent_server_notices.py
@@ -34,7 +34,7 @@ class ConsentServerNotices:
         self._server_notices_manager = hs.get_server_notices_manager()
         self._store = hs.get_datastore()
 
-        self._users_in_progress = set()  # type: Set[str]
+        self._users_in_progress: Set[str] = set()
 
         self._current_consent_version = hs.config.user_consent_version
         self._server_notice_content = hs.config.user_consent_server_notice_content
diff --git a/synapse/server_notices/resource_limits_server_notices.py b/synapse/server_notices/resource_limits_server_notices.py
index e4b0bc5c72..073b0d754f 100644
--- a/synapse/server_notices/resource_limits_server_notices.py
+++ b/synapse/server_notices/resource_limits_server_notices.py
@@ -205,7 +205,7 @@ class ResourceLimitsServerNotices:
             # The user has yet to join the server notices room
             pass
 
-        referenced_events = []  # type: List[str]
+        referenced_events: List[str] = []
         if pinned_state_event is not None:
             referenced_events = list(pinned_state_event.content.get("pinned", []))
 
diff --git a/synapse/server_notices/server_notices_sender.py b/synapse/server_notices/server_notices_sender.py
index c875b15b32..cdf0973d05 100644
--- a/synapse/server_notices/server_notices_sender.py
+++ b/synapse/server_notices/server_notices_sender.py
@@ -32,10 +32,12 @@ class ServerNoticesSender(WorkerServerNoticesSender):
 
     def __init__(self, hs: "HomeServer"):
         super().__init__(hs)
-        self._server_notices = (
+        self._server_notices: Iterable[
+            Union[ConsentServerNotices, ResourceLimitsServerNotices]
+        ] = (
             ConsentServerNotices(hs),
             ResourceLimitsServerNotices(hs),
-        )  # type: Iterable[Union[ConsentServerNotices, ResourceLimitsServerNotices]]
+        )
 
     async def on_user_syncing(self, user_id: str) -> None:
         """Called when the user performs a sync operation.
diff --git a/synapse/state/__init__.py b/synapse/state/__init__.py
index a1770f620e..6223daf522 100644
--- a/synapse/state/__init__.py
+++ b/synapse/state/__init__.py
@@ -309,9 +309,9 @@ class StateHandler:
 
         if old_state:
             # if we're given the state before the event, then we use that
-            state_ids_before_event = {
+            state_ids_before_event: StateMap[str] = {
                 (s.type, s.state_key): s.event_id for s in old_state
-            }  # type: StateMap[str]
+            }
             state_group_before_event = None
             state_group_before_event_prev_group = None
             deltas_to_state_group_before_event = None
@@ -513,23 +513,25 @@ class StateResolutionHandler:
         self.resolve_linearizer = Linearizer(name="state_resolve_lock")
 
         # dict of set of event_ids -> _StateCacheEntry.
-        self._state_cache = ExpiringCache(
+        self._state_cache: ExpiringCache[
+            FrozenSet[int], _StateCacheEntry
+        ] = ExpiringCache(
             cache_name="state_cache",
             clock=self.clock,
             max_len=100000,
             expiry_ms=EVICTION_TIMEOUT_SECONDS * 1000,
             iterable=True,
             reset_expiry_on_get=True,
-        )  # type: ExpiringCache[FrozenSet[int], _StateCacheEntry]
+        )
 
         #
         # stuff for tracking time spent on state-res by room
         #
 
         # tracks the amount of work done on state res per room
-        self._state_res_metrics = defaultdict(
+        self._state_res_metrics: DefaultDict[str, _StateResMetrics] = defaultdict(
             _StateResMetrics
-        )  # type: DefaultDict[str, _StateResMetrics]
+        )
 
         self.clock.looping_call(self._report_metrics, 120 * 1000)
 
@@ -700,9 +702,9 @@ class StateResolutionHandler:
         items = self._state_res_metrics.items()
 
         # log the N biggest rooms
-        biggest = heapq.nlargest(
+        biggest: List[Tuple[str, _StateResMetrics]] = heapq.nlargest(
             n_to_log, items, key=lambda i: extract_key(i[1])
-        )  # type: List[Tuple[str, _StateResMetrics]]
+        )
         metrics_logger.debug(
             "%i biggest rooms for state-res by %s: %s",
             len(biggest),
@@ -754,7 +756,7 @@ def _make_state_cache_entry(
 
     # failing that, look for the closest match.
     prev_group = None
-    delta_ids = None  # type: Optional[StateMap[str]]
+    delta_ids: Optional[StateMap[str]] = None
 
     for old_group, old_state in state_groups_ids.items():
         n_delta_ids = {k: v for k, v in new_state.items() if old_state.get(k) != v}
diff --git a/synapse/state/v1.py b/synapse/state/v1.py
index 318e998813..267193cedf 100644
--- a/synapse/state/v1.py
+++ b/synapse/state/v1.py
@@ -159,7 +159,7 @@ def _seperate(
     """
     state_set_iterator = iter(state_sets)
     unconflicted_state = dict(next(state_set_iterator))
-    conflicted_state = {}  # type: MutableStateMap[Set[str]]
+    conflicted_state: MutableStateMap[Set[str]] = {}
 
     for state_set in state_set_iterator:
         for key, value in state_set.items():
diff --git a/synapse/state/v2.py b/synapse/state/v2.py
index 008644cd98..e66e6571c8 100644
--- a/synapse/state/v2.py
+++ b/synapse/state/v2.py
@@ -276,7 +276,7 @@ async def _get_auth_chain_difference(
     # event IDs if they appear in the `event_map`. This is the intersection of
     # the event's auth chain with the events in the `event_map` *plus* their
     # auth event IDs.
-    events_to_auth_chain = {}  # type: Dict[str, Set[str]]
+    events_to_auth_chain: Dict[str, Set[str]] = {}
     for event in event_map.values():
         chain = {event.event_id}
         events_to_auth_chain[event.event_id] = chain
@@ -301,17 +301,17 @@ async def _get_auth_chain_difference(
         # ((type, state_key)->event_id) mappings; and (b) we have stripped out
         # unpersisted events and replaced them with the persisted events in
         # their auth chain.
-        state_sets_ids = []  # type: List[Set[str]]
+        state_sets_ids: List[Set[str]] = []
 
         # For each state set, the unpersisted event IDs reachable (by their auth
         # chain) from the events in that set.
-        unpersisted_set_ids = []  # type: List[Set[str]]
+        unpersisted_set_ids: List[Set[str]] = []
 
         for state_set in state_sets:
-            set_ids = set()  # type: Set[str]
+            set_ids: Set[str] = set()
             state_sets_ids.append(set_ids)
 
-            unpersisted_ids = set()  # type: Set[str]
+            unpersisted_ids: Set[str] = set()
             unpersisted_set_ids.append(unpersisted_ids)
 
             for event_id in state_set.values():
@@ -334,7 +334,7 @@ async def _get_auth_chain_difference(
         union = unpersisted_set_ids[0].union(*unpersisted_set_ids[1:])
         intersection = unpersisted_set_ids[0].intersection(*unpersisted_set_ids[1:])
 
-        difference_from_event_map = union - intersection  # type: Collection[str]
+        difference_from_event_map: Collection[str] = union - intersection
     else:
         difference_from_event_map = ()
         state_sets_ids = [set(state_set.values()) for state_set in state_sets]
@@ -458,7 +458,7 @@ async def _reverse_topological_power_sort(
         The sorted list
     """
 
-    graph = {}  # type: Dict[str, Set[str]]
+    graph: Dict[str, Set[str]] = {}
     for idx, event_id in enumerate(event_ids, start=1):
         await _add_event_and_auth_chain_to_graph(
             graph, room_id, event_id, event_map, state_res_store, auth_diff
@@ -657,7 +657,7 @@ async def _get_mainline_depth_for_event(
     """
 
     room_id = event.room_id
-    tmp_event = event  # type: Optional[EventBase]
+    tmp_event: Optional[EventBase] = event
 
     # We do an iterative search, replacing `event with the power level in its
     # auth events (if any)
@@ -767,7 +767,7 @@ def lexicographical_topological_sort(
     # outgoing edges, c.f.
     # https://en.wikipedia.org/wiki/Topological_sorting#Kahn's_algorithm
     outdegree_map = graph
-    reverse_graph = {}  # type: Dict[str, Set[str]]
+    reverse_graph: Dict[str, Set[str]] = {}
 
     # Lists of nodes with zero out degree. Is actually a tuple of
     # `(key(node), node)` so that sorting does the right thing
diff --git a/synapse/storage/databases/main/event_federation.py b/synapse/storage/databases/main/event_federation.py
index c4474df975..4e06938849 100644
--- a/synapse/storage/databases/main/event_federation.py
+++ b/synapse/storage/databases/main/event_federation.py
@@ -1230,7 +1230,9 @@ class EventFederationWorkerStore(EventsWorkerStore, SignatureWorkerStore, SQLBas
                 "SELECT coalesce(min(received_ts), 0) FROM federation_inbound_events_staging"
             )
 
-            (age,) = txn.fetchone()
+            (received_ts,) = txn.fetchone()
+
+            age = self._clock.time_msec() - received_ts
 
             return count, age
 
diff --git a/synapse/storage/databases/main/events.py b/synapse/storage/databases/main/events.py
index 897fa06639..08c580b0dc 100644
--- a/synapse/storage/databases/main/events.py
+++ b/synapse/storage/databases/main/events.py
@@ -1580,11 +1580,11 @@ class PersistEventsStore:
         # invalidate the cache for the redacted event
         txn.call_after(self.store._invalidate_get_event_cache, event.redacts)
 
-        self.db_pool.simple_insert_txn(
+        self.db_pool.simple_upsert_txn(
             txn,
             table="redactions",
+            keyvalues={"event_id": event.event_id},
             values={
-                "event_id": event.event_id,
                 "redacts": event.redacts,
                 "received_ts": self._clock.time_msec(),
             },
diff --git a/synapse/storage/databases/main/metrics.py b/synapse/storage/databases/main/metrics.py
index c3f551d377..e3a544d9b2 100644
--- a/synapse/storage/databases/main/metrics.py
+++ b/synapse/storage/databases/main/metrics.py
@@ -320,7 +320,7 @@ class ServerMetricsStore(EventPushActionsWorkerStore, SQLBaseStore):
         """
         Returns millisecond unixtime for start of UTC day.
         """
-        now = time.gmtime()
+        now = time.gmtime(self._clock.time())
         today_start = calendar.timegm((now.tm_year, now.tm_mon, now.tm_mday, 0, 0, 0))
         return today_start * 1000
 
@@ -352,7 +352,7 @@ class ServerMetricsStore(EventPushActionsWorkerStore, SQLBaseStore):
                     ) udv
                     ON u.user_id = udv.user_id AND u.device_id=udv.device_id
                     INNER JOIN users ON users.name=u.user_id
-                    WHERE last_seen > ? AND last_seen <= ?
+                    WHERE ? <= last_seen AND last_seen < ?
                     AND udv.timestamp IS NULL AND users.is_guest=0
                     AND users.appservice_id IS NULL
                     GROUP BY u.user_id, u.device_id
diff --git a/synapse/storage/databases/main/purge_events.py b/synapse/storage/databases/main/purge_events.py
index 7fb7780d0f..eb4841830d 100644
--- a/synapse/storage/databases/main/purge_events.py
+++ b/synapse/storage/databases/main/purge_events.py
@@ -215,6 +215,7 @@ class PurgeEventsStore(StateGroupWorkerStore, CacheInvalidationWorkerStore):
             "event_relations",
             "event_search",
             "rejections",
+            "redactions",
         ):
             logger.info("[purge] removing events from %s", table)
 
@@ -392,7 +393,6 @@ class PurgeEventsStore(StateGroupWorkerStore, CacheInvalidationWorkerStore):
             "room_memberships",
             "room_stats_state",
             "room_stats_current",
-            "room_stats_historical",
             "room_stats_earliest_token",
             "rooms",
             "stream_ordering_to_exterm",
diff --git a/synapse/storage/databases/main/room.py b/synapse/storage/databases/main/room.py
index 9f0d64a325..6ddafe5434 100644
--- a/synapse/storage/databases/main/room.py
+++ b/synapse/storage/databases/main/room.py
@@ -25,6 +25,7 @@ from synapse.api.room_versions import RoomVersion, RoomVersions
 from synapse.storage._base import SQLBaseStore, db_to_json
 from synapse.storage.database import DatabasePool, LoggingTransaction
 from synapse.storage.databases.main.search import SearchStore
+from synapse.storage.types import Cursor
 from synapse.types import JsonDict, ThirdPartyInstanceID
 from synapse.util import json_encoder
 from synapse.util.caches.descriptors import cached
@@ -1022,10 +1023,22 @@ class RoomWorkerStore(SQLBaseStore):
         )
 
 
-class RoomBackgroundUpdateStore(SQLBaseStore):
+class _BackgroundUpdates:
     REMOVE_TOMESTONED_ROOMS_BG_UPDATE = "remove_tombstoned_rooms_from_directory"
     ADD_ROOMS_ROOM_VERSION_COLUMN = "add_rooms_room_version_column"
+    POPULATE_ROOM_DEPTH_MIN_DEPTH2 = "populate_room_depth_min_depth2"
+    REPLACE_ROOM_DEPTH_MIN_DEPTH = "replace_room_depth_min_depth"
+
+
+_REPLACE_ROOM_DEPTH_SQL_COMMANDS = (
+    "DROP TRIGGER populate_min_depth2_trigger ON room_depth",
+    "DROP FUNCTION populate_min_depth2()",
+    "ALTER TABLE room_depth DROP COLUMN min_depth",
+    "ALTER TABLE room_depth RENAME COLUMN min_depth2 TO min_depth",
+)
+
 
+class RoomBackgroundUpdateStore(SQLBaseStore):
     def __init__(self, database: DatabasePool, db_conn, hs):
         super().__init__(database, db_conn, hs)
 
@@ -1037,15 +1050,25 @@ class RoomBackgroundUpdateStore(SQLBaseStore):
         )
 
         self.db_pool.updates.register_background_update_handler(
-            self.REMOVE_TOMESTONED_ROOMS_BG_UPDATE,
+            _BackgroundUpdates.REMOVE_TOMESTONED_ROOMS_BG_UPDATE,
             self._remove_tombstoned_rooms_from_directory,
         )
 
         self.db_pool.updates.register_background_update_handler(
-            self.ADD_ROOMS_ROOM_VERSION_COLUMN,
+            _BackgroundUpdates.ADD_ROOMS_ROOM_VERSION_COLUMN,
             self._background_add_rooms_room_version_column,
         )
 
+        # BG updates to change the type of room_depth.min_depth
+        self.db_pool.updates.register_background_update_handler(
+            _BackgroundUpdates.POPULATE_ROOM_DEPTH_MIN_DEPTH2,
+            self._background_populate_room_depth_min_depth2,
+        )
+        self.db_pool.updates.register_background_update_handler(
+            _BackgroundUpdates.REPLACE_ROOM_DEPTH_MIN_DEPTH,
+            self._background_replace_room_depth_min_depth,
+        )
+
     async def _background_insert_retention(self, progress, batch_size):
         """Retrieves a list of all rooms within a range and inserts an entry for each of
         them into the room_retention table.
@@ -1164,7 +1187,9 @@ class RoomBackgroundUpdateStore(SQLBaseStore):
                 new_last_room_id = room_id
 
             self.db_pool.updates._background_update_progress_txn(
-                txn, self.ADD_ROOMS_ROOM_VERSION_COLUMN, {"room_id": new_last_room_id}
+                txn,
+                _BackgroundUpdates.ADD_ROOMS_ROOM_VERSION_COLUMN,
+                {"room_id": new_last_room_id},
             )
 
             return False
@@ -1176,7 +1201,7 @@ class RoomBackgroundUpdateStore(SQLBaseStore):
 
         if end:
             await self.db_pool.updates._end_background_update(
-                self.ADD_ROOMS_ROOM_VERSION_COLUMN
+                _BackgroundUpdates.ADD_ROOMS_ROOM_VERSION_COLUMN
             )
 
         return batch_size
@@ -1215,7 +1240,7 @@ class RoomBackgroundUpdateStore(SQLBaseStore):
 
         if not rooms:
             await self.db_pool.updates._end_background_update(
-                self.REMOVE_TOMESTONED_ROOMS_BG_UPDATE
+                _BackgroundUpdates.REMOVE_TOMESTONED_ROOMS_BG_UPDATE
             )
             return 0
 
@@ -1224,7 +1249,7 @@ class RoomBackgroundUpdateStore(SQLBaseStore):
             await self.set_room_is_public(room_id, False)
 
         await self.db_pool.updates._background_update_progress(
-            self.REMOVE_TOMESTONED_ROOMS_BG_UPDATE, {"room_id": rooms[-1]}
+            _BackgroundUpdates.REMOVE_TOMESTONED_ROOMS_BG_UPDATE, {"room_id": rooms[-1]}
         )
 
         return len(rooms)
@@ -1268,6 +1293,71 @@ class RoomBackgroundUpdateStore(SQLBaseStore):
 
         return max_ordering is None
 
+    async def _background_populate_room_depth_min_depth2(
+        self, progress: JsonDict, batch_size: int
+    ) -> int:
+        """Populate room_depth.min_depth2
+
+        This is to deal with the fact that min_depth was initially created as a
+        32-bit integer field.
+        """
+
+        def process(txn: Cursor) -> int:
+            last_room = progress.get("last_room", "")
+            txn.execute(
+                """
+                UPDATE room_depth SET min_depth2=min_depth
+                WHERE room_id IN (
+                   SELECT room_id FROM room_depth WHERE room_id > ?
+                   ORDER BY room_id LIMIT ?
+                )
+                RETURNING room_id;
+                """,
+                (last_room, batch_size),
+            )
+            row_count = txn.rowcount
+            if row_count == 0:
+                return 0
+            last_room = max(row[0] for row in txn)
+            logger.info("populated room_depth up to %s", last_room)
+
+            self.db_pool.updates._background_update_progress_txn(
+                txn,
+                _BackgroundUpdates.POPULATE_ROOM_DEPTH_MIN_DEPTH2,
+                {"last_room": last_room},
+            )
+            return row_count
+
+        result = await self.db_pool.runInteraction(
+            "_background_populate_min_depth2", process
+        )
+
+        if result != 0:
+            return result
+
+        await self.db_pool.updates._end_background_update(
+            _BackgroundUpdates.POPULATE_ROOM_DEPTH_MIN_DEPTH2
+        )
+        return 0
+
+    async def _background_replace_room_depth_min_depth(
+        self, progress: JsonDict, batch_size: int
+    ) -> int:
+        """Drop the old 'min_depth' column and rename 'min_depth2' into its place."""
+
+        def process(txn: Cursor) -> None:
+            for sql in _REPLACE_ROOM_DEPTH_SQL_COMMANDS:
+                logger.info("completing room_depth migration: %s", sql)
+                txn.execute(sql)
+
+        await self.db_pool.runInteraction("_background_replace_room_depth", process)
+
+        await self.db_pool.updates._end_background_update(
+            _BackgroundUpdates.REPLACE_ROOM_DEPTH_MIN_DEPTH,
+        )
+
+        return 0
+
 
 class RoomStore(RoomBackgroundUpdateStore, RoomWorkerStore, SearchStore):
     def __init__(self, database: DatabasePool, db_conn, hs):
diff --git a/synapse/storage/databases/main/roommember.py b/synapse/storage/databases/main/roommember.py
index 2796354a1f..4d82c4c26d 100644
--- a/synapse/storage/databases/main/roommember.py
+++ b/synapse/storage/databases/main/roommember.py
@@ -703,13 +703,22 @@ class RoomMemberWorkerStore(EventsWorkerStore):
 
     @cached(max_entries=10000)
     async def is_host_joined(self, room_id: str, host: str) -> bool:
+        return await self._check_host_room_membership(room_id, host, Membership.JOIN)
+
+    @cached(max_entries=10000)
+    async def is_host_invited(self, room_id: str, host: str) -> bool:
+        return await self._check_host_room_membership(room_id, host, Membership.INVITE)
+
+    async def _check_host_room_membership(
+        self, room_id: str, host: str, membership: str
+    ) -> bool:
         if "%" in host or "_" in host:
             raise Exception("Invalid host name")
 
         sql = """
             SELECT state_key FROM current_state_events AS c
             INNER JOIN room_memberships AS m USING (event_id)
-            WHERE m.membership = 'join'
+            WHERE m.membership = ?
                 AND type = 'm.room.member'
                 AND c.room_id = ?
                 AND state_key LIKE ?
@@ -722,7 +731,7 @@ class RoomMemberWorkerStore(EventsWorkerStore):
         like_clause = "%:" + host
 
         rows = await self.db_pool.execute(
-            "is_host_joined", None, sql, room_id, like_clause
+            "is_host_joined", None, sql, membership, room_id, like_clause
         )
 
         if not rows:
diff --git a/synapse/storage/databases/main/stats.py b/synapse/storage/databases/main/stats.py
index 82a1833509..59d67c255b 100644
--- a/synapse/storage/databases/main/stats.py
+++ b/synapse/storage/databases/main/stats.py
@@ -26,7 +26,6 @@ from synapse.api.constants import EventTypes, Membership
 from synapse.api.errors import StoreError
 from synapse.storage.database import DatabasePool
 from synapse.storage.databases.main.state_deltas import StateDeltasStore
-from synapse.storage.engines import PostgresEngine
 from synapse.types import JsonDict
 from synapse.util.caches.descriptors import cached
 
@@ -49,14 +48,6 @@ ABSOLUTE_STATS_FIELDS = {
     "user": ("joined_rooms",),
 }
 
-# these fields are per-timeslice and so should be reset to 0 upon a new slice
-# You can draw these stats on a histogram.
-# Example: number of events sent locally during a time slice
-PER_SLICE_FIELDS = {
-    "room": ("total_events", "total_event_bytes"),
-    "user": ("invites_sent", "rooms_created", "total_events", "total_event_bytes"),
-}
-
 TYPE_TO_TABLE = {"room": ("room_stats", "room_id"), "user": ("user_stats", "user_id")}
 
 # these are the tables (& ID columns) which contain our actual subjects
@@ -106,7 +97,6 @@ class StatsStore(StateDeltasStore):
         self.server_name = hs.hostname
         self.clock = self.hs.get_clock()
         self.stats_enabled = hs.config.stats_enabled
-        self.stats_bucket_size = hs.config.stats_bucket_size
 
         self.stats_delta_processing_lock = DeferredLock()
 
@@ -122,22 +112,6 @@ class StatsStore(StateDeltasStore):
         self.db_pool.updates.register_noop_background_update("populate_stats_cleanup")
         self.db_pool.updates.register_noop_background_update("populate_stats_prepare")
 
-    def quantise_stats_time(self, ts):
-        """
-        Quantises a timestamp to be a multiple of the bucket size.
-
-        Args:
-            ts (int): the timestamp to quantise, in milliseconds since the Unix
-                Epoch
-
-        Returns:
-            int: a timestamp which
-              - is divisible by the bucket size;
-              - is no later than `ts`; and
-              - is the largest such timestamp.
-        """
-        return (ts // self.stats_bucket_size) * self.stats_bucket_size
-
     async def _populate_stats_process_users(self, progress, batch_size):
         """
         This is a background update which regenerates statistics for users.
@@ -288,56 +262,6 @@ class StatsStore(StateDeltasStore):
             desc="update_room_state",
         )
 
-    async def get_statistics_for_subject(
-        self, stats_type: str, stats_id: str, start: str, size: int = 100
-    ) -> List[dict]:
-        """
-        Get statistics for a given subject.
-
-        Args:
-            stats_type: The type of subject
-            stats_id: The ID of the subject (e.g. room_id or user_id)
-            start: Pagination start. Number of entries, not timestamp.
-            size: How many entries to return.
-
-        Returns:
-            A list of dicts, where the dict has the keys of
-            ABSOLUTE_STATS_FIELDS[stats_type],  and "bucket_size" and "end_ts".
-        """
-        return await self.db_pool.runInteraction(
-            "get_statistics_for_subject",
-            self._get_statistics_for_subject_txn,
-            stats_type,
-            stats_id,
-            start,
-            size,
-        )
-
-    def _get_statistics_for_subject_txn(
-        self, txn, stats_type, stats_id, start, size=100
-    ):
-        """
-        Transaction-bound version of L{get_statistics_for_subject}.
-        """
-
-        table, id_col = TYPE_TO_TABLE[stats_type]
-        selected_columns = list(
-            ABSOLUTE_STATS_FIELDS[stats_type] + PER_SLICE_FIELDS[stats_type]
-        )
-
-        slice_list = self.db_pool.simple_select_list_paginate_txn(
-            txn,
-            table + "_historical",
-            "end_ts",
-            start,
-            size,
-            retcols=selected_columns + ["bucket_size", "end_ts"],
-            keyvalues={id_col: stats_id},
-            order_direction="DESC",
-        )
-
-        return slice_list
-
     @cached()
     async def get_earliest_token_for_stats(
         self, stats_type: str, id: str
@@ -451,14 +375,10 @@ class StatsStore(StateDeltasStore):
 
         table, id_col = TYPE_TO_TABLE[stats_type]
 
-        quantised_ts = self.quantise_stats_time(int(ts))
-        end_ts = quantised_ts + self.stats_bucket_size
-
         # Lets be paranoid and check that all the given field names are known
         abs_field_names = ABSOLUTE_STATS_FIELDS[stats_type]
-        slice_field_names = PER_SLICE_FIELDS[stats_type]
         for field in chain(fields.keys(), absolute_field_overrides.keys()):
-            if field not in abs_field_names and field not in slice_field_names:
+            if field not in abs_field_names:
                 # guard against potential SQL injection dodginess
                 raise ValueError(
                     "%s is not a recognised field"
@@ -491,20 +411,6 @@ class StatsStore(StateDeltasStore):
             additive_relatives=deltas_of_absolute_fields,
         )
 
-        per_slice_additive_relatives = {
-            key: fields.get(key, 0) for key in slice_field_names
-        }
-        self._upsert_copy_from_table_with_additive_relatives_txn(
-            txn=txn,
-            into_table=table + "_historical",
-            keyvalues={id_col: stats_id},
-            extra_dst_insvalues={"bucket_size": self.stats_bucket_size},
-            extra_dst_keyvalues={"end_ts": end_ts},
-            additive_relatives=per_slice_additive_relatives,
-            src_table=table + "_current",
-            copy_columns=abs_field_names,
-        )
-
     def _upsert_with_additive_relatives_txn(
         self, txn, table, keyvalues, absolutes, additive_relatives
     ):
@@ -528,7 +434,7 @@ class StatsStore(StateDeltasStore):
             ]
 
             relative_updates = [
-                "%(field)s = EXCLUDED.%(field)s + %(table)s.%(field)s"
+                "%(field)s = EXCLUDED.%(field)s + COALESCE(%(table)s.%(field)s, 0)"
                 % {"table": table, "field": field}
                 for field in additive_relatives.keys()
             ]
@@ -568,205 +474,13 @@ class StatsStore(StateDeltasStore):
                 self.db_pool.simple_insert_txn(txn, table, merged_dict)
             else:
                 for (key, val) in additive_relatives.items():
-                    current_row[key] += val
+                    if current_row[key] is None:
+                        current_row[key] = val
+                    else:
+                        current_row[key] += val
                 current_row.update(absolutes)
                 self.db_pool.simple_update_one_txn(txn, table, keyvalues, current_row)
 
-    def _upsert_copy_from_table_with_additive_relatives_txn(
-        self,
-        txn,
-        into_table,
-        keyvalues,
-        extra_dst_keyvalues,
-        extra_dst_insvalues,
-        additive_relatives,
-        src_table,
-        copy_columns,
-    ):
-        """Updates the historic stats table with latest updates.
-
-        This involves copying "absolute" fields from the `_current` table, and
-        adding relative fields to any existing values.
-
-        Args:
-             txn: Transaction
-             into_table (str): The destination table to UPSERT the row into
-             keyvalues (dict[str, any]): Row-identifying key values
-             extra_dst_keyvalues (dict[str, any]): Additional keyvalues
-                for `into_table`.
-             extra_dst_insvalues (dict[str, any]): Additional values to insert
-                on new row creation for `into_table`.
-             additive_relatives (dict[str, any]): Fields that will be added onto
-                if existing row present. (Must be disjoint from copy_columns.)
-             src_table (str): The source table to copy from
-             copy_columns (iterable[str]): The list of columns to copy
-        """
-        if self.database_engine.can_native_upsert:
-            ins_columns = chain(
-                keyvalues,
-                copy_columns,
-                additive_relatives,
-                extra_dst_keyvalues,
-                extra_dst_insvalues,
-            )
-            sel_exprs = chain(
-                keyvalues,
-                copy_columns,
-                (
-                    "?"
-                    for _ in chain(
-                        additive_relatives, extra_dst_keyvalues, extra_dst_insvalues
-                    )
-                ),
-            )
-            keyvalues_where = ("%s = ?" % f for f in keyvalues)
-
-            sets_cc = ("%s = EXCLUDED.%s" % (f, f) for f in copy_columns)
-            sets_ar = (
-                "%s = EXCLUDED.%s + %s.%s" % (f, f, into_table, f)
-                for f in additive_relatives
-            )
-
-            sql = """
-                INSERT INTO %(into_table)s (%(ins_columns)s)
-                SELECT %(sel_exprs)s
-                FROM %(src_table)s
-                WHERE %(keyvalues_where)s
-                ON CONFLICT (%(keyvalues)s)
-                DO UPDATE SET %(sets)s
-            """ % {
-                "into_table": into_table,
-                "ins_columns": ", ".join(ins_columns),
-                "sel_exprs": ", ".join(sel_exprs),
-                "keyvalues_where": " AND ".join(keyvalues_where),
-                "src_table": src_table,
-                "keyvalues": ", ".join(
-                    chain(keyvalues.keys(), extra_dst_keyvalues.keys())
-                ),
-                "sets": ", ".join(chain(sets_cc, sets_ar)),
-            }
-
-            qargs = list(
-                chain(
-                    additive_relatives.values(),
-                    extra_dst_keyvalues.values(),
-                    extra_dst_insvalues.values(),
-                    keyvalues.values(),
-                )
-            )
-            txn.execute(sql, qargs)
-        else:
-            self.database_engine.lock_table(txn, into_table)
-            src_row = self.db_pool.simple_select_one_txn(
-                txn, src_table, keyvalues, copy_columns
-            )
-            all_dest_keyvalues = {**keyvalues, **extra_dst_keyvalues}
-            dest_current_row = self.db_pool.simple_select_one_txn(
-                txn,
-                into_table,
-                keyvalues=all_dest_keyvalues,
-                retcols=list(chain(additive_relatives.keys(), copy_columns)),
-                allow_none=True,
-            )
-
-            if dest_current_row is None:
-                merged_dict = {
-                    **keyvalues,
-                    **extra_dst_keyvalues,
-                    **extra_dst_insvalues,
-                    **src_row,
-                    **additive_relatives,
-                }
-                self.db_pool.simple_insert_txn(txn, into_table, merged_dict)
-            else:
-                for (key, val) in additive_relatives.items():
-                    src_row[key] = dest_current_row[key] + val
-                self.db_pool.simple_update_txn(
-                    txn, into_table, all_dest_keyvalues, src_row
-                )
-
-    async def get_changes_room_total_events_and_bytes(
-        self, min_pos: int, max_pos: int
-    ) -> Tuple[Dict[str, Dict[str, int]], Dict[str, Dict[str, int]]]:
-        """Fetches the counts of events in the given range of stream IDs.
-
-        Args:
-            min_pos
-            max_pos
-
-        Returns:
-            Mapping of room ID to field changes.
-        """
-
-        return await self.db_pool.runInteraction(
-            "stats_incremental_total_events_and_bytes",
-            self.get_changes_room_total_events_and_bytes_txn,
-            min_pos,
-            max_pos,
-        )
-
-    def get_changes_room_total_events_and_bytes_txn(
-        self, txn, low_pos: int, high_pos: int
-    ) -> Tuple[Dict[str, Dict[str, int]], Dict[str, Dict[str, int]]]:
-        """Gets the total_events and total_event_bytes counts for rooms and
-        senders, in a range of stream_orderings (including backfilled events).
-
-        Args:
-            txn
-            low_pos: Low stream ordering
-            high_pos: High stream ordering
-
-        Returns:
-            The room and user deltas for total_events/total_event_bytes in the
-            format of `stats_id` -> fields
-        """
-
-        if low_pos >= high_pos:
-            # nothing to do here.
-            return {}, {}
-
-        if isinstance(self.database_engine, PostgresEngine):
-            new_bytes_expression = "OCTET_LENGTH(json)"
-        else:
-            new_bytes_expression = "LENGTH(CAST(json AS BLOB))"
-
-        sql = """
-            SELECT events.room_id, COUNT(*) AS new_events, SUM(%s) AS new_bytes
-            FROM events INNER JOIN event_json USING (event_id)
-            WHERE (? < stream_ordering AND stream_ordering <= ?)
-                OR (? <= stream_ordering AND stream_ordering <= ?)
-            GROUP BY events.room_id
-        """ % (
-            new_bytes_expression,
-        )
-
-        txn.execute(sql, (low_pos, high_pos, -high_pos, -low_pos))
-
-        room_deltas = {
-            room_id: {"total_events": new_events, "total_event_bytes": new_bytes}
-            for room_id, new_events, new_bytes in txn
-        }
-
-        sql = """
-            SELECT events.sender, COUNT(*) AS new_events, SUM(%s) AS new_bytes
-            FROM events INNER JOIN event_json USING (event_id)
-            WHERE (? < stream_ordering AND stream_ordering <= ?)
-                OR (? <= stream_ordering AND stream_ordering <= ?)
-            GROUP BY events.sender
-        """ % (
-            new_bytes_expression,
-        )
-
-        txn.execute(sql, (low_pos, high_pos, -high_pos, -low_pos))
-
-        user_deltas = {
-            user_id: {"total_events": new_events, "total_event_bytes": new_bytes}
-            for user_id, new_events, new_bytes in txn
-            if self.hs.is_mine_id(user_id)
-        }
-
-        return room_deltas, user_deltas
-
     async def _calculate_and_set_initial_state_for_room(
         self, room_id: str
     ) -> Tuple[dict, dict, int]:
@@ -893,6 +607,7 @@ class StatsStore(StateDeltasStore):
                 "invited_members": membership_counts.get(Membership.INVITE, 0),
                 "left_members": membership_counts.get(Membership.LEAVE, 0),
                 "banned_members": membership_counts.get(Membership.BAN, 0),
+                "knocked_members": membership_counts.get(Membership.KNOCK, 0),
                 "local_users_in_room": len(local_users_in_room),
             },
         )
diff --git a/synapse/storage/schema/__init__.py b/synapse/storage/schema/__init__.py
index 0a53b73ccc..36340a652a 100644
--- a/synapse/storage/schema/__init__.py
+++ b/synapse/storage/schema/__init__.py
@@ -12,7 +12,7 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
-SCHEMA_VERSION = 60
+SCHEMA_VERSION = 61
 """Represents the expectations made by the codebase about the database schema
 
 This should be incremented whenever the codebase changes its requirements on the
@@ -21,6 +21,10 @@ older versions of Synapse).
 
 See `README.md <synapse/storage/schema/README.md>`_  for more information on how this
 works.
+
+Changes in SCHEMA_VERSION = 61:
+    - The `user_stats_historical` and `room_stats_historical` tables are not written and
+      are not read (previously, they were written but not read).
 """
 
 
diff --git a/synapse/storage/schema/main/delta/61/01change_appservices_txns.sql.postgres b/synapse/storage/schema/main/delta/61/01change_appservices_txns.sql.postgres
new file mode 100644
index 0000000000..c8aec78e60
--- /dev/null
+++ b/synapse/storage/schema/main/delta/61/01change_appservices_txns.sql.postgres
@@ -0,0 +1,23 @@
+/* Copyright 2021 The Matrix.org Foundation C.I.C
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *    http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+-- we use bigint elsewhere in the database for appservice txn ids (notably,
+-- application_services_state.last_txn), and generally we use bigints everywhere else
+-- we have monotonic counters, so let's bring this one in line.
+--
+-- assuming there aren't thousands of rows for decommisioned/non-functional ASes, this
+-- table should be pretty small, so safe to do a synchronous ALTER TABLE.
+
+ALTER TABLE application_services_txns ALTER COLUMN txn_id SET DATA TYPE BIGINT;
diff --git a/synapse/storage/schema/main/delta/61/02drop_redundant_room_depth_index.sql b/synapse/storage/schema/main/delta/61/02drop_redundant_room_depth_index.sql
new file mode 100644
index 0000000000..35ca7a40c0
--- /dev/null
+++ b/synapse/storage/schema/main/delta/61/02drop_redundant_room_depth_index.sql
@@ -0,0 +1,18 @@
+/* Copyright 2021 The Matrix.org Foundation C.I.C
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *    http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+-- this index is redundant; there is another UNIQUE index on this table.
+DROP INDEX IF EXISTS room_depth_room;
+
diff --git a/synapse/storage/schema/main/delta/61/03recreate_min_depth.py b/synapse/storage/schema/main/delta/61/03recreate_min_depth.py
new file mode 100644
index 0000000000..f8d7db9f2e
--- /dev/null
+++ b/synapse/storage/schema/main/delta/61/03recreate_min_depth.py
@@ -0,0 +1,70 @@
+# Copyright 2021 The Matrix.org Foundation C.I.C.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+"""
+This migration handles the process of changing the type of `room_depth.min_depth` to
+a BIGINT.
+"""
+from synapse.storage.engines import BaseDatabaseEngine, PostgresEngine
+from synapse.storage.types import Cursor
+
+
+def run_create(cur: Cursor, database_engine: BaseDatabaseEngine, *args, **kwargs):
+    if not isinstance(database_engine, PostgresEngine):
+        # this only applies to postgres - sqlite does not distinguish between big and
+        # little ints.
+        return
+
+    # First add a new column to contain the bigger min_depth
+    cur.execute("ALTER TABLE room_depth ADD COLUMN min_depth2 BIGINT")
+
+    # Create a trigger which will keep it populated.
+    cur.execute(
+        """
+        CREATE OR REPLACE FUNCTION populate_min_depth2() RETURNS trigger AS $BODY$
+            BEGIN
+                new.min_depth2 := new.min_depth;
+                RETURN NEW;
+            END;
+        $BODY$ LANGUAGE plpgsql
+        """
+    )
+
+    cur.execute(
+        """
+        CREATE TRIGGER populate_min_depth2_trigger BEFORE INSERT OR UPDATE ON room_depth
+        FOR EACH ROW
+        EXECUTE PROCEDURE populate_min_depth2()
+        """
+    )
+
+    # Start a bg process to populate it for old rooms
+    cur.execute(
+        """
+       INSERT INTO background_updates (ordering, update_name, progress_json) VALUES
+            (6103, 'populate_room_depth_min_depth2', '{}')
+       """
+    )
+
+    # and another to switch them over once it completes.
+    cur.execute(
+        """
+        INSERT INTO background_updates (ordering, update_name, progress_json, depends_on) VALUES
+            (6103, 'replace_room_depth_min_depth', '{}', 'populate_room_depth2')
+        """
+    )
+
+
+def run_upgrade(cur: Cursor, database_engine: BaseDatabaseEngine, *args, **kwargs):
+    pass
diff --git a/synapse/streams/events.py b/synapse/streams/events.py
index 20fceaa935..99b0aac2fb 100644
--- a/synapse/streams/events.py
+++ b/synapse/streams/events.py
@@ -32,9 +32,9 @@ class EventSources:
     }
 
     def __init__(self, hs):
-        self.sources = {
+        self.sources: Dict[str, Any] = {
             name: cls(hs) for name, cls in EventSources.SOURCE_TYPES.items()
-        }  # type: Dict[str, Any]
+        }
         self.store = hs.get_datastore()
 
     def get_current_token(self) -> StreamToken:
diff --git a/synapse/types.py b/synapse/types.py
index 8d2fa00f71..fad23c8700 100644
--- a/synapse/types.py
+++ b/synapse/types.py
@@ -182,14 +182,14 @@ def create_requester(
     )
 
 
-def get_domain_from_id(string):
+def get_domain_from_id(string: str) -> str:
     idx = string.find(":")
     if idx == -1:
         raise SynapseError(400, "Invalid ID: %r" % (string,))
     return string[idx + 1 :]
 
 
-def get_localpart_from_id(string):
+def get_localpart_from_id(string: str) -> str:
     idx = string.find(":")
     if idx == -1:
         raise SynapseError(400, "Invalid ID: %r" % (string,))
@@ -210,7 +210,7 @@ class DomainSpecificString(metaclass=abc.ABCMeta):
         'domain' : The domain part of the name
     """
 
-    SIGIL = abc.abstractproperty()  # type: str  # type: ignore
+    SIGIL: str = abc.abstractproperty()  # type: ignore
 
     localpart = attr.ib(type=str)
     domain = attr.ib(type=str)
@@ -304,7 +304,7 @@ class GroupID(DomainSpecificString):
 
     @classmethod
     def from_string(cls: Type[DS], s: str) -> DS:
-        group_id = super().from_string(s)  # type: DS # type: ignore
+        group_id: DS = super().from_string(s)  # type: ignore
 
         if not group_id.localpart:
             raise SynapseError(400, "Group ID cannot be empty", Codes.INVALID_PARAM)
@@ -600,7 +600,7 @@ class StreamToken:
     groups_key = attr.ib(type=int)
 
     _SEPARATOR = "_"
-    START = None  # type: StreamToken
+    START: "StreamToken"
 
     @classmethod
     async def from_string(cls, store: "DataStore", string: str) -> "StreamToken":
diff --git a/synapse/visibility.py b/synapse/visibility.py
index 490fb26e81..1dc6b90275 100644
--- a/synapse/visibility.py
+++ b/synapse/visibility.py
@@ -90,7 +90,7 @@ async def filter_events_for_client(
         AccountDataTypes.IGNORED_USER_LIST, user_id
     )
 
-    ignore_list = frozenset()  # type: FrozenSet[str]
+    ignore_list: FrozenSet[str] = frozenset()
     if ignore_dict_content:
         ignored_users_dict = ignore_dict_content.get("ignored_users", {})
         if isinstance(ignored_users_dict, dict):