Merge branch 'develop' into jaywink/admin-forward-extremities

39 files changed, 2048 insertions, 410 deletions

diff --git a/synapse/storage/database.py b/synapse/storage/database.py
index b70ca3087b..d2ba4bd2fc 100644
--- a/synapse/storage/database.py
+++ b/synapse/storage/database.py
@@ -49,6 +49,7 @@ from synapse.metrics.background_process_metrics import run_as_background_process
 from synapse.storage.background_updates import BackgroundUpdater
 from synapse.storage.engines import BaseDatabaseEngine, PostgresEngine, Sqlite3Engine
 from synapse.storage.types import Connection, Cursor
+from synapse.storage.util.sequence import build_sequence_generator
 from synapse.types import Collection
 
 # python 3 does not have a maximum int value
@@ -179,6 +180,9 @@ class LoggingDatabaseConnection:
 _CallbackListEntry = Tuple["Callable[..., None]", Iterable[Any], Dict[str, Any]]
 
 
+R = TypeVar("R")
+
+
 class LoggingTransaction:
     """An object that almost-transparently proxies for the 'txn' object
     passed to the constructor. Adds logging and metrics to the .execute()
@@ -258,13 +262,32 @@ class LoggingTransaction:
         return self.txn.description
 
     def execute_batch(self, sql: str, args: Iterable[Iterable[Any]]) -> None:
+        """Similar to `executemany`, except `txn.rowcount` will not be correct
+        afterwards.
+
+        More efficient than `executemany` on PostgreSQL
+        """
+
         if isinstance(self.database_engine, PostgresEngine):
             from psycopg2.extras import execute_batch  # type: ignore
 
             self._do_execute(lambda *x: execute_batch(self.txn, *x), sql, args)
         else:
-            for val in args:
-                self.execute(sql, val)
+            self.executemany(sql, args)
+
+    def execute_values(self, sql: str, *args: Any) -> List[Tuple]:
+        """Corresponds to psycopg2.extras.execute_values. Only available when
+        using postgres.
+
+        Always sets fetch=True when caling `execute_values`, so will return the
+        results.
+        """
+        assert isinstance(self.database_engine, PostgresEngine)
+        from psycopg2.extras import execute_values  # type: ignore
+
+        return self._do_execute(
+            lambda *x: execute_values(self.txn, *x, fetch=True), sql, *args
+        )
 
     def execute(self, sql: str, *args: Any) -> None:
         self._do_execute(self.txn.execute, sql, *args)
@@ -276,7 +299,7 @@ class LoggingTransaction:
         "Strip newlines out of SQL so that the loggers in the DB are on one line"
         return " ".join(line.strip() for line in sql.splitlines() if line.strip())
 
-    def _do_execute(self, func, sql: str, *args: Any) -> None:
+    def _do_execute(self, func: Callable[..., R], sql: str, *args: Any) -> R:
         sql = self._make_sql_one_line(sql)
 
         # TODO(paul): Maybe use 'info' and 'debug' for values?
@@ -347,9 +370,6 @@ class PerformanceCounters:
         return top_n_counters
 
 
-R = TypeVar("R")
-
-
 class DatabasePool:
     """Wraps a single physical database and connection pool.
 
@@ -398,6 +418,16 @@ class DatabasePool:
                 self._check_safe_to_upsert,
             )
 
+        # We define this sequence here so that it can be referenced from both
+        # the DataStore and PersistEventStore.
+        def get_chain_id_txn(txn):
+            txn.execute("SELECT COALESCE(max(chain_id), 0) FROM event_auth_chains")
+            return txn.fetchone()[0]
+
+        self.event_chain_id_gen = build_sequence_generator(
+            engine, get_chain_id_txn, "event_auth_chain_id"
+        )
+
     def is_running(self) -> bool:
         """Is the database pool currently running
         """
@@ -863,7 +893,7 @@ class DatabasePool:
             ", ".join("?" for _ in keys[0]),
         )
 
-        txn.executemany(sql, vals)
+        txn.execute_batch(sql, vals)
 
     async def simple_upsert(
         self,
diff --git a/synapse/storage/databases/main/__init__.py b/synapse/storage/databases/main/__init__.py
index b936f54f1e..5d0845588c 100644
--- a/synapse/storage/databases/main/__init__.py
+++ b/synapse/storage/databases/main/__init__.py
@@ -162,9 +162,13 @@ class DataStore(
                 database,
                 stream_name="caches",
                 instance_name=hs.get_instance_name(),
-                table="cache_invalidation_stream_by_instance",
-                instance_column="instance_name",
-                id_column="stream_id",
+                tables=[
+                    (
+                        "cache_invalidation_stream_by_instance",
+                        "instance_name",
+                        "stream_id",
+                    )
+                ],
                 sequence_name="cache_invalidation_stream_seq",
                 writers=[],
             )
diff --git a/synapse/storage/databases/main/account_data.py b/synapse/storage/databases/main/account_data.py
index bff51e92b9..a277a1ef13 100644
--- a/synapse/storage/databases/main/account_data.py
+++ b/synapse/storage/databases/main/account_data.py
@@ -14,14 +14,16 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
-import abc
 import logging
 from typing import Dict, List, Optional, Set, Tuple
 
 from synapse.api.constants import AccountDataTypes
+from synapse.replication.slave.storage._slaved_id_tracker import SlavedIdTracker
+from synapse.replication.tcp.streams import AccountDataStream, TagAccountDataStream
 from synapse.storage._base import SQLBaseStore, db_to_json
 from synapse.storage.database import DatabasePool
-from synapse.storage.util.id_generators import StreamIdGenerator
+from synapse.storage.engines import PostgresEngine
+from synapse.storage.util.id_generators import MultiWriterIdGenerator, StreamIdGenerator
 from synapse.types import JsonDict
 from synapse.util import json_encoder
 from synapse.util.caches.descriptors import cached
@@ -30,14 +32,57 @@ from synapse.util.caches.stream_change_cache import StreamChangeCache
 logger = logging.getLogger(__name__)
 
 
-# The ABCMeta metaclass ensures that it cannot be instantiated without
-# the abstract methods being implemented.
-class AccountDataWorkerStore(SQLBaseStore, metaclass=abc.ABCMeta):
+class AccountDataWorkerStore(SQLBaseStore):
     """This is an abstract base class where subclasses must implement
     `get_max_account_data_stream_id` which can be called in the initializer.
     """
 
     def __init__(self, database: DatabasePool, db_conn, hs):
+        self._instance_name = hs.get_instance_name()
+
+        if isinstance(database.engine, PostgresEngine):
+            self._can_write_to_account_data = (
+                self._instance_name in hs.config.worker.writers.account_data
+            )
+
+            self._account_data_id_gen = MultiWriterIdGenerator(
+                db_conn=db_conn,
+                db=database,
+                stream_name="account_data",
+                instance_name=self._instance_name,
+                tables=[
+                    ("room_account_data", "instance_name", "stream_id"),
+                    ("room_tags_revisions", "instance_name", "stream_id"),
+                    ("account_data", "instance_name", "stream_id"),
+                ],
+                sequence_name="account_data_sequence",
+                writers=hs.config.worker.writers.account_data,
+            )
+        else:
+            self._can_write_to_account_data = True
+
+            # We shouldn't be running in worker mode with SQLite, but its useful
+            # to support it for unit tests.
+            #
+            # If this process is the writer than we need to use
+            # `StreamIdGenerator`, otherwise we use `SlavedIdTracker` which gets
+            # updated over replication. (Multiple writers are not supported for
+            # SQLite).
+            if hs.get_instance_name() in hs.config.worker.writers.account_data:
+                self._account_data_id_gen = StreamIdGenerator(
+                    db_conn,
+                    "room_account_data",
+                    "stream_id",
+                    extra_tables=[("room_tags_revisions", "stream_id")],
+                )
+            else:
+                self._account_data_id_gen = SlavedIdTracker(
+                    db_conn,
+                    "room_account_data",
+                    "stream_id",
+                    extra_tables=[("room_tags_revisions", "stream_id")],
+                )
+
         account_max = self.get_max_account_data_stream_id()
         self._account_data_stream_cache = StreamChangeCache(
             "AccountDataAndTagsChangeCache", account_max
@@ -45,14 +90,13 @@ class AccountDataWorkerStore(SQLBaseStore, metaclass=abc.ABCMeta):
 
         super().__init__(database, db_conn, hs)
 
-    @abc.abstractmethod
-    def get_max_account_data_stream_id(self):
+    def get_max_account_data_stream_id(self) -> int:
         """Get the current max stream ID for account data stream
 
         Returns:
             int
         """
-        raise NotImplementedError()
+        return self._account_data_id_gen.get_current_token()
 
     @cached()
     async def get_account_data_for_user(
@@ -307,28 +351,26 @@ class AccountDataWorkerStore(SQLBaseStore, metaclass=abc.ABCMeta):
             )
         )
 
-
-class AccountDataStore(AccountDataWorkerStore):
-    def __init__(self, database: DatabasePool, db_conn, hs):
-        self._account_data_id_gen = StreamIdGenerator(
-            db_conn,
-            "account_data_max_stream_id",
-            "stream_id",
-            extra_tables=[
-                ("room_account_data", "stream_id"),
-                ("room_tags_revisions", "stream_id"),
-            ],
-        )
-
-        super().__init__(database, db_conn, hs)
-
-    def get_max_account_data_stream_id(self) -> int:
-        """Get the current max stream id for the private user data stream
-
-        Returns:
-            The maximum stream ID.
-        """
-        return self._account_data_id_gen.get_current_token()
+    def process_replication_rows(self, stream_name, instance_name, token, rows):
+        if stream_name == TagAccountDataStream.NAME:
+            self._account_data_id_gen.advance(instance_name, token)
+            for row in rows:
+                self.get_tags_for_user.invalidate((row.user_id,))
+                self._account_data_stream_cache.entity_has_changed(row.user_id, token)
+        elif stream_name == AccountDataStream.NAME:
+            self._account_data_id_gen.advance(instance_name, token)
+            for row in rows:
+                if not row.room_id:
+                    self.get_global_account_data_by_type_for_user.invalidate(
+                        (row.data_type, row.user_id)
+                    )
+                self.get_account_data_for_user.invalidate((row.user_id,))
+                self.get_account_data_for_room.invalidate((row.user_id, row.room_id))
+                self.get_account_data_for_room_and_type.invalidate(
+                    (row.user_id, row.room_id, row.data_type)
+                )
+                self._account_data_stream_cache.entity_has_changed(row.user_id, token)
+        return super().process_replication_rows(stream_name, instance_name, token, rows)
 
     async def add_account_data_to_room(
         self, user_id: str, room_id: str, account_data_type: str, content: JsonDict
@@ -344,6 +386,8 @@ class AccountDataStore(AccountDataWorkerStore):
         Returns:
             The maximum stream ID.
         """
+        assert self._can_write_to_account_data
+
         content_json = json_encoder.encode(content)
 
         async with self._account_data_id_gen.get_next() as next_id:
@@ -362,14 +406,6 @@ class AccountDataStore(AccountDataWorkerStore):
                 lock=False,
             )
 
-            # it's theoretically possible for the above to succeed and the
-            # below to fail - in which case we might reuse a stream id on
-            # restart, and the above update might not get propagated. That
-            # doesn't sound any worse than the whole update getting lost,
-            # which is what would happen if we combined the two into one
-            # transaction.
-            await self._update_max_stream_id(next_id)
-
             self._account_data_stream_cache.entity_has_changed(user_id, next_id)
             self.get_account_data_for_user.invalidate((user_id,))
             self.get_account_data_for_room.invalidate((user_id, room_id))
@@ -392,6 +428,8 @@ class AccountDataStore(AccountDataWorkerStore):
         Returns:
             The maximum stream ID.
         """
+        assert self._can_write_to_account_data
+
         async with self._account_data_id_gen.get_next() as next_id:
             await self.db_pool.runInteraction(
                 "add_user_account_data",
@@ -402,18 +440,6 @@ class AccountDataStore(AccountDataWorkerStore):
                 content,
             )
 
-            # it's theoretically possible for the above to succeed and the
-            # below to fail - in which case we might reuse a stream id on
-            # restart, and the above update might not get propagated. That
-            # doesn't sound any worse than the whole update getting lost,
-            # which is what would happen if we combined the two into one
-            # transaction.
-            #
-            # Note: This is only here for backwards compat to allow admins to
-            # roll back to a previous Synapse version. Next time we update the
-            # database version we can remove this table.
-            await self._update_max_stream_id(next_id)
-
             self._account_data_stream_cache.entity_has_changed(user_id, next_id)
             self.get_account_data_for_user.invalidate((user_id,))
             self.get_global_account_data_by_type_for_user.invalidate(
@@ -487,23 +513,6 @@ class AccountDataStore(AccountDataWorkerStore):
         for ignored_user_id in previously_ignored_users ^ currently_ignored_users:
             self._invalidate_cache_and_stream(txn, self.ignored_by, (ignored_user_id,))
 
-    async def _update_max_stream_id(self, next_id: int) -> None:
-        """Update the max stream_id
-
-        Args:
-            next_id: The the revision to advance to.
-        """
 
-        # Note: This is only here for backwards compat to allow admins to
-        # roll back to a previous Synapse version. Next time we update the
-        # database version we can remove this table.
-
-        def _update(txn):
-            update_max_id_sql = (
-                "UPDATE account_data_max_stream_id"
-                " SET stream_id = ?"
-                " WHERE stream_id < ?"
-            )
-            txn.execute(update_max_id_sql, (next_id, next_id))
-
-        await self.db_pool.runInteraction("update_account_data_max_stream_id", _update)
+class AccountDataStore(AccountDataWorkerStore):
+    pass
diff --git a/synapse/storage/databases/main/client_ips.py b/synapse/storage/databases/main/client_ips.py
index c53c836337..ea1e8fb580 100644
--- a/synapse/storage/databases/main/client_ips.py
+++ b/synapse/storage/databases/main/client_ips.py
@@ -407,6 +407,34 @@ class ClientIpWorkerStore(ClientIpBackgroundUpdateStore):
             "_prune_old_user_ips", _prune_old_user_ips_txn
         )
 
+    async def get_last_client_ip_by_device(
+        self, user_id: str, device_id: Optional[str]
+    ) -> Dict[Tuple[str, str], dict]:
+        """For each device_id listed, give the user_ip it was last seen on.
+
+        The result might be slightly out of date as client IPs are inserted in batches.
+
+        Args:
+            user_id: The user to fetch devices for.
+            device_id: If None fetches all devices for the user
+
+        Returns:
+            A dictionary mapping a tuple of (user_id, device_id) to dicts, with
+            keys giving the column names from the devices table.
+        """
+
+        keyvalues = {"user_id": user_id}
+        if device_id is not None:
+            keyvalues["device_id"] = device_id
+
+        res = await self.db_pool.simple_select_list(
+            table="devices",
+            keyvalues=keyvalues,
+            retcols=("user_id", "ip", "user_agent", "device_id", "last_seen"),
+        )
+
+        return {(d["user_id"], d["device_id"]): d for d in res}
+
 
 class ClientIpStore(ClientIpWorkerStore):
     def __init__(self, database: DatabasePool, db_conn, hs):
@@ -512,18 +540,9 @@ class ClientIpStore(ClientIpWorkerStore):
             A dictionary mapping a tuple of (user_id, device_id) to dicts, with
             keys giving the column names from the devices table.
         """
+        ret = await super().get_last_client_ip_by_device(user_id, device_id)
 
-        keyvalues = {"user_id": user_id}
-        if device_id is not None:
-            keyvalues["device_id"] = device_id
-
-        res = await self.db_pool.simple_select_list(
-            table="devices",
-            keyvalues=keyvalues,
-            retcols=("user_id", "ip", "user_agent", "device_id", "last_seen"),
-        )
-
-        ret = {(d["user_id"], d["device_id"]): d for d in res}
+        # Update what is retrieved from the database with data which is pending insertion.
         for key in self._batch_row_update:
             uid, access_token, ip = key
             if uid == user_id:
diff --git a/synapse/storage/databases/main/deviceinbox.py b/synapse/storage/databases/main/deviceinbox.py
index 58d3f71e45..31f70ac5ef 100644
--- a/synapse/storage/databases/main/deviceinbox.py
+++ b/synapse/storage/databases/main/deviceinbox.py
@@ -54,9 +54,7 @@ class DeviceInboxWorkerStore(SQLBaseStore):
                 db=database,
                 stream_name="to_device",
                 instance_name=self._instance_name,
-                table="device_inbox",
-                instance_column="instance_name",
-                id_column="stream_id",
+                tables=[("device_inbox", "instance_name", "stream_id")],
                 sequence_name="device_inbox_sequence",
                 writers=hs.config.worker.writers.to_device,
             )
diff --git a/synapse/storage/databases/main/devices.py b/synapse/storage/databases/main/devices.py
index 9097677648..659d8f245f 100644
--- a/synapse/storage/databases/main/devices.py
+++ b/synapse/storage/databases/main/devices.py
@@ -897,7 +897,7 @@ class DeviceWorkerStore(SQLBaseStore):
                 DELETE FROM device_lists_outbound_last_success
                 WHERE destination = ? AND user_id = ?
             """
-            txn.executemany(sql, ((row[0], row[1]) for row in rows))
+            txn.execute_batch(sql, ((row[0], row[1]) for row in rows))
 
             logger.info("Pruned %d device list outbound pokes", count)
 
@@ -1343,7 +1343,7 @@ class DeviceStore(DeviceWorkerStore, DeviceBackgroundUpdateStore):
 
         # Delete older entries in the table, as we really only care about
         # when the latest change happened.
-        txn.executemany(
+        txn.execute_batch(
             """
             DELETE FROM device_lists_stream
             WHERE user_id = ? AND device_id = ? AND stream_id < ?
diff --git a/synapse/storage/databases/main/end_to_end_keys.py b/synapse/storage/databases/main/end_to_end_keys.py
index 4d1b92d1aa..c128889bf9 100644
--- a/synapse/storage/databases/main/end_to_end_keys.py
+++ b/synapse/storage/databases/main/end_to_end_keys.py
@@ -25,6 +25,7 @@ from twisted.enterprise.adbapi import Connection
 from synapse.logging.opentracing import log_kv, set_tag, trace
 from synapse.storage._base import SQLBaseStore, db_to_json
 from synapse.storage.database import DatabasePool, make_in_list_sql_clause
+from synapse.storage.engines import PostgresEngine
 from synapse.storage.types import Cursor
 from synapse.types import JsonDict
 from synapse.util import json_encoder
@@ -513,21 +514,35 @@ class EndToEndKeyWorkerStore(EndToEndKeyBackgroundStore):
 
         for user_chunk in batch_iter(user_ids, 100):
             clause, params = make_in_list_sql_clause(
-                txn.database_engine, "k.user_id", user_chunk
-            )
-            sql = (
-                """
-                SELECT k.user_id, k.keytype, k.keydata, k.stream_id
-                  FROM e2e_cross_signing_keys k
-                  INNER JOIN (SELECT user_id, keytype, MAX(stream_id) AS stream_id
-                                FROM e2e_cross_signing_keys
-                               GROUP BY user_id, keytype) s
-                 USING (user_id, stream_id, keytype)
-                 WHERE
-            """
-                + clause
+                txn.database_engine, "user_id", user_chunk
             )
 
+            # Fetch the latest key for each type per user.
+            if isinstance(self.database_engine, PostgresEngine):
+                # The `DISTINCT ON` clause will pick the *first* row it
+                # encounters, so ordering by stream ID desc will ensure we get
+                # the latest key.
+                sql = """
+                    SELECT DISTINCT ON (user_id, keytype) user_id, keytype, keydata, stream_id
+                        FROM e2e_cross_signing_keys
+                        WHERE %(clause)s
+                        ORDER BY user_id, keytype, stream_id DESC
+                """ % {
+                    "clause": clause
+                }
+            else:
+                # SQLite has special handling for bare columns when using
+                # MIN/MAX with a `GROUP BY` clause where it picks the value from
+                # a row that matches the MIN/MAX.
+                sql = """
+                    SELECT user_id, keytype, keydata, MAX(stream_id)
+                        FROM e2e_cross_signing_keys
+                        WHERE %(clause)s
+                        GROUP BY user_id, keytype
+                """ % {
+                    "clause": clause
+                }
+
             txn.execute(sql, params)
             rows = self.db_pool.cursor_to_dict(txn)
 
@@ -707,50 +722,6 @@ class EndToEndKeyWorkerStore(EndToEndKeyBackgroundStore):
         """Get the current stream id from the _device_list_id_gen"""
         ...
 
-
-class EndToEndKeyStore(EndToEndKeyWorkerStore, SQLBaseStore):
-    async def set_e2e_device_keys(
-        self, user_id: str, device_id: str, time_now: int, device_keys: JsonDict
-    ) -> bool:
-        """Stores device keys for a device. Returns whether there was a change
-        or the keys were already in the database.
-        """
-
-        def _set_e2e_device_keys_txn(txn):
-            set_tag("user_id", user_id)
-            set_tag("device_id", device_id)
-            set_tag("time_now", time_now)
-            set_tag("device_keys", device_keys)
-
-            old_key_json = self.db_pool.simple_select_one_onecol_txn(
-                txn,
-                table="e2e_device_keys_json",
-                keyvalues={"user_id": user_id, "device_id": device_id},
-                retcol="key_json",
-                allow_none=True,
-            )
-
-            # In py3 we need old_key_json to match new_key_json type. The DB
-            # returns unicode while encode_canonical_json returns bytes.
-            new_key_json = encode_canonical_json(device_keys).decode("utf-8")
-
-            if old_key_json == new_key_json:
-                log_kv({"Message": "Device key already stored."})
-                return False
-
-            self.db_pool.simple_upsert_txn(
-                txn,
-                table="e2e_device_keys_json",
-                keyvalues={"user_id": user_id, "device_id": device_id},
-                values={"ts_added_ms": time_now, "key_json": new_key_json},
-            )
-            log_kv({"message": "Device keys stored."})
-            return True
-
-        return await self.db_pool.runInteraction(
-            "set_e2e_device_keys", _set_e2e_device_keys_txn
-        )
-
     async def claim_e2e_one_time_keys(
         self, query_list: Iterable[Tuple[str, str, str]]
     ) -> Dict[str, Dict[str, Dict[str, bytes]]]:
@@ -840,6 +811,50 @@ class EndToEndKeyStore(EndToEndKeyWorkerStore, SQLBaseStore):
             "claim_e2e_one_time_keys", _claim_e2e_one_time_keys
         )
 
+
+class EndToEndKeyStore(EndToEndKeyWorkerStore, SQLBaseStore):
+    async def set_e2e_device_keys(
+        self, user_id: str, device_id: str, time_now: int, device_keys: JsonDict
+    ) -> bool:
+        """Stores device keys for a device. Returns whether there was a change
+        or the keys were already in the database.
+        """
+
+        def _set_e2e_device_keys_txn(txn):
+            set_tag("user_id", user_id)
+            set_tag("device_id", device_id)
+            set_tag("time_now", time_now)
+            set_tag("device_keys", device_keys)
+
+            old_key_json = self.db_pool.simple_select_one_onecol_txn(
+                txn,
+                table="e2e_device_keys_json",
+                keyvalues={"user_id": user_id, "device_id": device_id},
+                retcol="key_json",
+                allow_none=True,
+            )
+
+            # In py3 we need old_key_json to match new_key_json type. The DB
+            # returns unicode while encode_canonical_json returns bytes.
+            new_key_json = encode_canonical_json(device_keys).decode("utf-8")
+
+            if old_key_json == new_key_json:
+                log_kv({"Message": "Device key already stored."})
+                return False
+
+            self.db_pool.simple_upsert_txn(
+                txn,
+                table="e2e_device_keys_json",
+                keyvalues={"user_id": user_id, "device_id": device_id},
+                values={"ts_added_ms": time_now, "key_json": new_key_json},
+            )
+            log_kv({"message": "Device keys stored."})
+            return True
+
+        return await self.db_pool.runInteraction(
+            "set_e2e_device_keys", _set_e2e_device_keys_txn
+        )
+
     async def delete_e2e_keys_by_device(self, user_id: str, device_id: str) -> None:
         def delete_e2e_keys_by_device_txn(txn):
             log_kv(
diff --git a/synapse/storage/databases/main/event_federation.py b/synapse/storage/databases/main/event_federation.py
index ebffd89251..8326640d20 100644
--- a/synapse/storage/databases/main/event_federation.py
+++ b/synapse/storage/databases/main/event_federation.py
@@ -24,6 +24,8 @@ from synapse.storage._base import SQLBaseStore, make_in_list_sql_clause
 from synapse.storage.database import DatabasePool, LoggingTransaction
 from synapse.storage.databases.main.events_worker import EventsWorkerStore
 from synapse.storage.databases.main.signatures import SignatureWorkerStore
+from synapse.storage.engines import PostgresEngine
+from synapse.storage.types import Cursor
 from synapse.types import Collection
 from synapse.util.caches.descriptors import cached
 from synapse.util.caches.lrucache import LruCache
@@ -32,6 +34,11 @@ from synapse.util.iterutils import batch_iter
 logger = logging.getLogger(__name__)
 
 
+class _NoChainCoverIndex(Exception):
+    def __init__(self, room_id: str):
+        super().__init__("Unexpectedly no chain cover for events in %s" % (room_id,))
+
+
 class EventFederationWorkerStore(EventsWorkerStore, SignatureWorkerStore, SQLBaseStore):
     def __init__(self, database: DatabasePool, db_conn, hs):
         super().__init__(database, db_conn, hs)
@@ -151,15 +158,193 @@ class EventFederationWorkerStore(EventsWorkerStore, SignatureWorkerStore, SQLBas
             The set of the difference in auth chains.
         """
 
+        # Check if we have indexed the room so we can use the chain cover
+        # algorithm.
+        room = await self.get_room(room_id)
+        if room["has_auth_chain_index"]:
+            try:
+                return await self.db_pool.runInteraction(
+                    "get_auth_chain_difference_chains",
+                    self._get_auth_chain_difference_using_cover_index_txn,
+                    room_id,
+                    state_sets,
+                )
+            except _NoChainCoverIndex:
+                # For whatever reason we don't actually have a chain cover index
+                # for the events in question, so we fall back to the old method.
+                pass
+
         return await self.db_pool.runInteraction(
             "get_auth_chain_difference",
             self._get_auth_chain_difference_txn,
             state_sets,
         )
 
+    def _get_auth_chain_difference_using_cover_index_txn(
+        self, txn: Cursor, room_id: str, state_sets: List[Set[str]]
+    ) -> Set[str]:
+        """Calculates the auth chain difference using the chain index.
+
+        See docs/auth_chain_difference_algorithm.md for details
+        """
+
+        # First we look up the chain ID/sequence numbers for all the events, and
+        # work out the chain/sequence numbers reachable from each state set.
+
+        initial_events = set(state_sets[0]).union(*state_sets[1:])
+
+        # Map from event_id -> (chain ID, seq no)
+        chain_info = {}  # type: Dict[str, Tuple[int, int]]
+
+        # Map from chain ID -> seq no -> event Id
+        chain_to_event = {}  # type: Dict[int, Dict[int, str]]
+
+        # All the chains that we've found that are reachable from the state
+        # sets.
+        seen_chains = set()  # type: Set[int]
+
+        sql = """
+            SELECT event_id, chain_id, sequence_number
+            FROM event_auth_chains
+            WHERE %s
+        """
+        for batch in batch_iter(initial_events, 1000):
+            clause, args = make_in_list_sql_clause(
+                txn.database_engine, "event_id", batch
+            )
+            txn.execute(sql % (clause,), args)
+
+            for event_id, chain_id, sequence_number in txn:
+                chain_info[event_id] = (chain_id, sequence_number)
+                seen_chains.add(chain_id)
+                chain_to_event.setdefault(chain_id, {})[sequence_number] = event_id
+
+        # Check that we actually have a chain ID for all the events.
+        events_missing_chain_info = initial_events.difference(chain_info)
+        if events_missing_chain_info:
+            # This can happen due to e.g. downgrade/upgrade of the server. We
+            # raise an exception and fall back to the previous algorithm.
+            logger.info(
+                "Unexpectedly found that events don't have chain IDs in room %s: %s",
+                room_id,
+                events_missing_chain_info,
+            )
+            raise _NoChainCoverIndex(room_id)
+
+        # Corresponds to `state_sets`, except as a map from chain ID to max
+        # sequence number reachable from the state set.
+        set_to_chain = []  # type: List[Dict[int, int]]
+        for state_set in state_sets:
+            chains = {}  # type: Dict[int, int]
+            set_to_chain.append(chains)
+
+            for event_id in state_set:
+                chain_id, seq_no = chain_info[event_id]
+
+                chains[chain_id] = max(seq_no, chains.get(chain_id, 0))
+
+        # Now we look up all links for the chains we have, adding chains to
+        # set_to_chain that are reachable from each set.
+        sql = """
+            SELECT
+                origin_chain_id, origin_sequence_number,
+                target_chain_id, target_sequence_number
+            FROM event_auth_chain_links
+            WHERE %s
+        """
+
+        # (We need to take a copy of `seen_chains` as we want to mutate it in
+        # the loop)
+        for batch in batch_iter(set(seen_chains), 1000):
+            clause, args = make_in_list_sql_clause(
+                txn.database_engine, "origin_chain_id", batch
+            )
+            txn.execute(sql % (clause,), args)
+
+            for (
+                origin_chain_id,
+                origin_sequence_number,
+                target_chain_id,
+                target_sequence_number,
+            ) in txn:
+                for chains in set_to_chain:
+                    # chains are only reachable if the origin sequence number of
+                    # the link is less than the max sequence number in the
+                    # origin chain.
+                    if origin_sequence_number <= chains.get(origin_chain_id, 0):
+                        chains[target_chain_id] = max(
+                            target_sequence_number, chains.get(target_chain_id, 0),
+                        )
+
+                seen_chains.add(target_chain_id)
+
+        # Now for each chain we figure out the maximum sequence number reachable
+        # from *any* state set and the minimum sequence number reachable from
+        # *all* state sets. Events in that range are in the auth chain
+        # difference.
+        result = set()
+
+        # Mapping from chain ID to the range of sequence numbers that should be
+        # pulled from the database.
+        chain_to_gap = {}  # type: Dict[int, Tuple[int, int]]
+
+        for chain_id in seen_chains:
+            min_seq_no = min(chains.get(chain_id, 0) for chains in set_to_chain)
+            max_seq_no = max(chains.get(chain_id, 0) for chains in set_to_chain)
+
+            if min_seq_no < max_seq_no:
+                # We have a non empty gap, try and fill it from the events that
+                # we have, otherwise add them to the list of gaps to pull out
+                # from the DB.
+                for seq_no in range(min_seq_no + 1, max_seq_no + 1):
+                    event_id = chain_to_event.get(chain_id, {}).get(seq_no)
+                    if event_id:
+                        result.add(event_id)
+                    else:
+                        chain_to_gap[chain_id] = (min_seq_no, max_seq_no)
+                        break
+
+        if not chain_to_gap:
+            # If there are no gaps to fetch, we're done!
+            return result
+
+        if isinstance(self.database_engine, PostgresEngine):
+            # We can use `execute_values` to efficiently fetch the gaps when
+            # using postgres.
+            sql = """
+                SELECT event_id
+                FROM event_auth_chains AS c, (VALUES ?) AS l(chain_id, min_seq, max_seq)
+                WHERE
+                    c.chain_id = l.chain_id
+                    AND min_seq < sequence_number AND sequence_number <= max_seq
+            """
+
+            args = [
+                (chain_id, min_no, max_no)
+                for chain_id, (min_no, max_no) in chain_to_gap.items()
+            ]
+
+            rows = txn.execute_values(sql, args)
+            result.update(r for r, in rows)
+        else:
+            # For SQLite we just fall back to doing a noddy for loop.
+            sql = """
+                SELECT event_id FROM event_auth_chains
+                WHERE chain_id = ? AND ? < sequence_number AND sequence_number <= ?
+            """
+            for chain_id, (min_no, max_no) in chain_to_gap.items():
+                txn.execute(sql, (chain_id, min_no, max_no))
+                result.update(r for r, in txn)
+
+        return result
+
     def _get_auth_chain_difference_txn(
         self, txn, state_sets: List[Set[str]]
     ) -> Set[str]:
+        """Calculates the auth chain difference using a breadth first search.
+
+        This is used when we don't have a cover index for the room.
+        """
 
         # Algorithm Description
         # ~~~~~~~~~~~~~~~~~~~~~
diff --git a/synapse/storage/databases/main/event_push_actions.py b/synapse/storage/databases/main/event_push_actions.py
index e5c03cc609..438383abe1 100644
--- a/synapse/storage/databases/main/event_push_actions.py
+++ b/synapse/storage/databases/main/event_push_actions.py
@@ -487,7 +487,7 @@ class EventPushActionsWorkerStore(SQLBaseStore):
                 VALUES (?, ?, ?, ?, ?, ?)
             """
 
-            txn.executemany(
+            txn.execute_batch(
                 sql,
                 (
                     _gen_entry(user_id, actions)
@@ -803,7 +803,7 @@ class EventPushActionsWorkerStore(SQLBaseStore):
             ],
         )
 
-        txn.executemany(
+        txn.execute_batch(
             """
                 UPDATE event_push_summary
                 SET notif_count = ?, unread_count = ?, stream_ordering = ?
@@ -835,6 +835,52 @@ class EventPushActionsWorkerStore(SQLBaseStore):
             (rotate_to_stream_ordering,),
         )
 
+    def _remove_old_push_actions_before_txn(
+        self, txn, room_id, user_id, stream_ordering
+    ):
+        """
+        Purges old push actions for a user and room before a given
+        stream_ordering.
+
+        We however keep a months worth of highlighted notifications, so that
+        users can still get a list of recent highlights.
+
+        Args:
+            txn: The transcation
+            room_id: Room ID to delete from
+            user_id: user ID to delete for
+            stream_ordering: The lowest stream ordering which will
+                                  not be deleted.
+        """
+        txn.call_after(
+            self.get_unread_event_push_actions_by_room_for_user.invalidate_many,
+            (room_id, user_id),
+        )
+
+        # We need to join on the events table to get the received_ts for
+        # event_push_actions and sqlite won't let us use a join in a delete so
+        # we can't just delete where received_ts < x. Furthermore we can
+        # only identify event_push_actions by a tuple of room_id, event_id
+        # we we can't use a subquery.
+        # Instead, we look up the stream ordering for the last event in that
+        # room received before the threshold time and delete event_push_actions
+        # in the room with a stream_odering before that.
+        txn.execute(
+            "DELETE FROM event_push_actions "
+            " WHERE user_id = ? AND room_id = ? AND "
+            " stream_ordering <= ?"
+            " AND ((stream_ordering < ? AND highlight = 1) or highlight = 0)",
+            (user_id, room_id, stream_ordering, self.stream_ordering_month_ago),
+        )
+
+        txn.execute(
+            """
+            DELETE FROM event_push_summary
+            WHERE room_id = ? AND user_id = ? AND stream_ordering <= ?
+        """,
+            (room_id, user_id, stream_ordering),
+        )
+
 
 class EventPushActionsStore(EventPushActionsWorkerStore):
     EPA_HIGHLIGHT_INDEX = "epa_highlight_index"
@@ -894,52 +940,6 @@ class EventPushActionsStore(EventPushActionsWorkerStore):
             pa["actions"] = _deserialize_action(pa["actions"], pa["highlight"])
         return push_actions
 
-    def _remove_old_push_actions_before_txn(
-        self, txn, room_id, user_id, stream_ordering
-    ):
-        """
-        Purges old push actions for a user and room before a given
-        stream_ordering.
-
-        We however keep a months worth of highlighted notifications, so that
-        users can still get a list of recent highlights.
-
-        Args:
-            txn: The transcation
-            room_id: Room ID to delete from
-            user_id: user ID to delete for
-            stream_ordering: The lowest stream ordering which will
-                                  not be deleted.
-        """
-        txn.call_after(
-            self.get_unread_event_push_actions_by_room_for_user.invalidate_many,
-            (room_id, user_id),
-        )
-
-        # We need to join on the events table to get the received_ts for
-        # event_push_actions and sqlite won't let us use a join in a delete so
-        # we can't just delete where received_ts < x. Furthermore we can
-        # only identify event_push_actions by a tuple of room_id, event_id
-        # we we can't use a subquery.
-        # Instead, we look up the stream ordering for the last event in that
-        # room received before the threshold time and delete event_push_actions
-        # in the room with a stream_odering before that.
-        txn.execute(
-            "DELETE FROM event_push_actions "
-            " WHERE user_id = ? AND room_id = ? AND "
-            " stream_ordering <= ?"
-            " AND ((stream_ordering < ? AND highlight = 1) or highlight = 0)",
-            (user_id, room_id, stream_ordering, self.stream_ordering_month_ago),
-        )
-
-        txn.execute(
-            """
-            DELETE FROM event_push_summary
-            WHERE room_id = ? AND user_id = ? AND stream_ordering <= ?
-        """,
-            (room_id, user_id, stream_ordering),
-        )
-
 
 def _action_has_highlight(actions):
     for action in actions:
diff --git a/synapse/storage/databases/main/events.py b/synapse/storage/databases/main/events.py
index 90fb1a1f00..ccda9f1caa 100644
--- a/synapse/storage/databases/main/events.py
+++ b/synapse/storage/databases/main/events.py
@@ -17,7 +17,17 @@
 import itertools
 import logging
 from collections import OrderedDict, namedtuple
-from typing import TYPE_CHECKING, Any, Dict, Iterable, List, Optional, Set, Tuple
+from typing import (
+    TYPE_CHECKING,
+    Any,
+    Dict,
+    Generator,
+    Iterable,
+    List,
+    Optional,
+    Set,
+    Tuple,
+)
 
 import attr
 from prometheus_client import Counter
@@ -35,7 +45,7 @@ from synapse.storage.databases.main.search import SearchEntry
 from synapse.storage.util.id_generators import MultiWriterIdGenerator
 from synapse.types import StateMap, get_domain_from_id
 from synapse.util import json_encoder
-from synapse.util.iterutils import batch_iter
+from synapse.util.iterutils import batch_iter, sorted_topologically
 
 if TYPE_CHECKING:
     from synapse.server import HomeServer
@@ -366,6 +376,36 @@ class PersistEventsStore:
         # Insert into event_to_state_groups.
         self._store_event_state_mappings_txn(txn, events_and_contexts)
 
+        self._persist_event_auth_chain_txn(txn, [e for e, _ in events_and_contexts])
+
+        # _store_rejected_events_txn filters out any events which were
+        # rejected, and returns the filtered list.
+        events_and_contexts = self._store_rejected_events_txn(
+            txn, events_and_contexts=events_and_contexts
+        )
+
+        # From this point onwards the events are only ones that weren't
+        # rejected.
+
+        self._update_metadata_tables_txn(
+            txn,
+            events_and_contexts=events_and_contexts,
+            all_events_and_contexts=all_events_and_contexts,
+            backfilled=backfilled,
+        )
+
+        # We call this last as it assumes we've inserted the events into
+        # room_memberships, where applicable.
+        self._update_current_state_txn(txn, state_delta_for_room, min_stream_order)
+
+    def _persist_event_auth_chain_txn(
+        self, txn: LoggingTransaction, events: List[EventBase],
+    ) -> None:
+
+        # We only care about state events, so this if there are no state events.
+        if not any(e.is_state() for e in events):
+            return
+
         # We want to store event_auth mappings for rejected events, as they're
         # used in state res v2.
         # This is only necessary if the rejected event appears in an accepted
@@ -381,31 +421,467 @@ class PersistEventsStore:
                     "room_id": event.room_id,
                     "auth_id": auth_id,
                 }
-                for event, _ in events_and_contexts
+                for event in events
                 for auth_id in event.auth_event_ids()
                 if event.is_state()
             ],
         )
 
-        # _store_rejected_events_txn filters out any events which were
-        # rejected, and returns the filtered list.
-        events_and_contexts = self._store_rejected_events_txn(
-            txn, events_and_contexts=events_and_contexts
+        # We now calculate chain ID/sequence numbers for any state events we're
+        # persisting. We ignore out of band memberships as we're not in the room
+        # and won't have their auth chain (we'll fix it up later if we join the
+        # room).
+        #
+        # See: docs/auth_chain_difference_algorithm.md
+
+        # We ignore legacy rooms that we aren't filling the chain cover index
+        # for.
+        rows = self.db_pool.simple_select_many_txn(
+            txn,
+            table="rooms",
+            column="room_id",
+            iterable={event.room_id for event in events if event.is_state()},
+            keyvalues={},
+            retcols=("room_id", "has_auth_chain_index"),
         )
+        rooms_using_chain_index = {
+            row["room_id"] for row in rows if row["has_auth_chain_index"]
+        }
 
-        # From this point onwards the events are only ones that weren't
-        # rejected.
+        state_events = {
+            event.event_id: event
+            for event in events
+            if event.is_state() and event.room_id in rooms_using_chain_index
+        }
 
-        self._update_metadata_tables_txn(
+        if not state_events:
+            return
+
+        # We need to know the type/state_key and auth events of the events we're
+        # calculating chain IDs for. We don't rely on having the full Event
+        # instances as we'll potentially be pulling more events from the DB and
+        # we don't need the overhead of fetching/parsing the full event JSON.
+        event_to_types = {
+            e.event_id: (e.type, e.state_key) for e in state_events.values()
+        }
+        event_to_auth_chain = {
+            e.event_id: e.auth_event_ids() for e in state_events.values()
+        }
+        event_to_room_id = {e.event_id: e.room_id for e in state_events.values()}
+
+        self._add_chain_cover_index(
+            txn, self.db_pool, event_to_room_id, event_to_types, event_to_auth_chain,
+        )
+
+    @classmethod
+    def _add_chain_cover_index(
+        cls,
+        txn,
+        db_pool: DatabasePool,
+        event_to_room_id: Dict[str, str],
+        event_to_types: Dict[str, Tuple[str, str]],
+        event_to_auth_chain: Dict[str, List[str]],
+    ) -> None:
+        """Calculate the chain cover index for the given events.
+
+        Args:
+            event_to_room_id: Event ID to the room ID of the event
+            event_to_types: Event ID to type and state_key of the event
+            event_to_auth_chain: Event ID to list of auth event IDs of the
+                event (events with no auth events can be excluded).
+        """
+
+        # Map from event ID to chain ID/sequence number.
+        chain_map = {}  # type: Dict[str, Tuple[int, int]]
+
+        # Set of event IDs to calculate chain ID/seq numbers for.
+        events_to_calc_chain_id_for = set(event_to_room_id)
+
+        # We check if there are any events that need to be handled in the rooms
+        # we're looking at. These should just be out of band memberships, where
+        # we didn't have the auth chain when we first persisted.
+        rows = db_pool.simple_select_many_txn(
             txn,
-            events_and_contexts=events_and_contexts,
-            all_events_and_contexts=all_events_and_contexts,
-            backfilled=backfilled,
+            table="event_auth_chain_to_calculate",
+            keyvalues={},
+            column="room_id",
+            iterable=set(event_to_room_id.values()),
+            retcols=("event_id", "type", "state_key"),
         )
+        for row in rows:
+            event_id = row["event_id"]
+            event_type = row["type"]
+            state_key = row["state_key"]
+
+            # (We could pull out the auth events for all rows at once using
+            # simple_select_many, but this case happens rarely and almost always
+            # with a single row.)
+            auth_events = db_pool.simple_select_onecol_txn(
+                txn, "event_auth", keyvalues={"event_id": event_id}, retcol="auth_id",
+            )
 
-        # We call this last as it assumes we've inserted the events into
-        # room_memberships, where applicable.
-        self._update_current_state_txn(txn, state_delta_for_room, min_stream_order)
+            events_to_calc_chain_id_for.add(event_id)
+            event_to_types[event_id] = (event_type, state_key)
+            event_to_auth_chain[event_id] = auth_events
+
+        # First we get the chain ID and sequence numbers for the events'
+        # auth events (that aren't also currently being persisted).
+        #
+        # Note that there there is an edge case here where we might not have
+        # calculated chains and sequence numbers for events that were "out
+        # of band". We handle this case by fetching the necessary info and
+        # adding it to the set of events to calculate chain IDs for.
+
+        missing_auth_chains = {
+            a_id
+            for auth_events in event_to_auth_chain.values()
+            for a_id in auth_events
+            if a_id not in events_to_calc_chain_id_for
+        }
+
+        # We loop here in case we find an out of band membership and need to
+        # fetch their auth event info.
+        while missing_auth_chains:
+            sql = """
+                SELECT event_id, events.type, state_key, chain_id, sequence_number
+                FROM events
+                INNER JOIN state_events USING (event_id)
+                LEFT JOIN event_auth_chains USING (event_id)
+                WHERE
+            """
+            clause, args = make_in_list_sql_clause(
+                txn.database_engine, "event_id", missing_auth_chains,
+            )
+            txn.execute(sql + clause, args)
+
+            missing_auth_chains.clear()
+
+            for auth_id, event_type, state_key, chain_id, sequence_number in txn:
+                event_to_types[auth_id] = (event_type, state_key)
+
+                if chain_id is None:
+                    # No chain ID, so the event was persisted out of band.
+                    # We add to list of events to calculate auth chains for.
+
+                    events_to_calc_chain_id_for.add(auth_id)
+
+                    event_to_auth_chain[auth_id] = db_pool.simple_select_onecol_txn(
+                        txn,
+                        "event_auth",
+                        keyvalues={"event_id": auth_id},
+                        retcol="auth_id",
+                    )
+
+                    missing_auth_chains.update(
+                        e
+                        for e in event_to_auth_chain[auth_id]
+                        if e not in event_to_types
+                    )
+                else:
+                    chain_map[auth_id] = (chain_id, sequence_number)
+
+        # Now we check if we have any events where we don't have auth chain,
+        # this should only be out of band memberships.
+        for event_id in sorted_topologically(event_to_auth_chain, event_to_auth_chain):
+            for auth_id in event_to_auth_chain[event_id]:
+                if (
+                    auth_id not in chain_map
+                    and auth_id not in events_to_calc_chain_id_for
+                ):
+                    events_to_calc_chain_id_for.discard(event_id)
+
+                    # If this is an event we're trying to persist we add it to
+                    # the list of events to calculate chain IDs for next time
+                    # around. (Otherwise we will have already added it to the
+                    # table).
+                    room_id = event_to_room_id.get(event_id)
+                    if room_id:
+                        e_type, state_key = event_to_types[event_id]
+                        db_pool.simple_insert_txn(
+                            txn,
+                            table="event_auth_chain_to_calculate",
+                            values={
+                                "event_id": event_id,
+                                "room_id": room_id,
+                                "type": e_type,
+                                "state_key": state_key,
+                            },
+                        )
+
+                    # We stop checking the event's auth events since we've
+                    # discarded it.
+                    break
+
+        if not events_to_calc_chain_id_for:
+            return
+
+        # Allocate chain ID/sequence numbers to each new event.
+        new_chain_tuples = cls._allocate_chain_ids(
+            txn,
+            db_pool,
+            event_to_room_id,
+            event_to_types,
+            event_to_auth_chain,
+            events_to_calc_chain_id_for,
+            chain_map,
+        )
+        chain_map.update(new_chain_tuples)
+
+        db_pool.simple_insert_many_txn(
+            txn,
+            table="event_auth_chains",
+            values=[
+                {"event_id": event_id, "chain_id": c_id, "sequence_number": seq}
+                for event_id, (c_id, seq) in new_chain_tuples.items()
+            ],
+        )
+
+        db_pool.simple_delete_many_txn(
+            txn,
+            table="event_auth_chain_to_calculate",
+            keyvalues={},
+            column="event_id",
+            iterable=new_chain_tuples,
+        )
+
+        # Now we need to calculate any new links between chains caused by
+        # the new events.
+        #
+        # Links are pairs of chain ID/sequence numbers such that for any
+        # event A (CA, SA) and any event B (CB, SB), B is in A's auth chain
+        # if and only if there is at least one link (CA, S1) -> (CB, S2)
+        # where SA >= S1 and S2 >= SB.
+        #
+        # We try and avoid adding redundant links to the table, e.g. if we
+        # have two links between two chains which both start/end at the
+        # sequence number event (or cross) then one can be safely dropped.
+        #
+        # To calculate new links we look at every new event and:
+        #   1. Fetch the chain ID/sequence numbers of its auth events,
+        #      discarding any that are reachable by other auth events, or
+        #      that have the same chain ID as the event.
+        #   2. For each retained auth event we:
+        #       a. Add a link from the event's to the auth event's chain
+        #          ID/sequence number; and
+        #       b. Add a link from the event to every chain reachable by the
+        #          auth event.
+
+        # Step 1, fetch all existing links from all the chains we've seen
+        # referenced.
+        chain_links = _LinkMap()
+        rows = db_pool.simple_select_many_txn(
+            txn,
+            table="event_auth_chain_links",
+            column="origin_chain_id",
+            iterable={chain_id for chain_id, _ in chain_map.values()},
+            keyvalues={},
+            retcols=(
+                "origin_chain_id",
+                "origin_sequence_number",
+                "target_chain_id",
+                "target_sequence_number",
+            ),
+        )
+        for row in rows:
+            chain_links.add_link(
+                (row["origin_chain_id"], row["origin_sequence_number"]),
+                (row["target_chain_id"], row["target_sequence_number"]),
+                new=False,
+            )
+
+        # We do this in toplogical order to avoid adding redundant links.
+        for event_id in sorted_topologically(
+            events_to_calc_chain_id_for, event_to_auth_chain
+        ):
+            chain_id, sequence_number = chain_map[event_id]
+
+            # Filter out auth events that are reachable by other auth
+            # events. We do this by looking at every permutation of pairs of
+            # auth events (A, B) to check if B is reachable from A.
+            reduction = {
+                a_id
+                for a_id in event_to_auth_chain.get(event_id, [])
+                if chain_map[a_id][0] != chain_id
+            }
+            for start_auth_id, end_auth_id in itertools.permutations(
+                event_to_auth_chain.get(event_id, []), r=2,
+            ):
+                if chain_links.exists_path_from(
+                    chain_map[start_auth_id], chain_map[end_auth_id]
+                ):
+                    reduction.discard(end_auth_id)
+
+            # Step 2, figure out what the new links are from the reduced
+            # list of auth events.
+            for auth_id in reduction:
+                auth_chain_id, auth_sequence_number = chain_map[auth_id]
+
+                # Step 2a, add link between the event and auth event
+                chain_links.add_link(
+                    (chain_id, sequence_number), (auth_chain_id, auth_sequence_number)
+                )
+
+                # Step 2b, add a link to chains reachable from the auth
+                # event.
+                for target_id, target_seq in chain_links.get_links_from(
+                    (auth_chain_id, auth_sequence_number)
+                ):
+                    if target_id == chain_id:
+                        continue
+
+                    chain_links.add_link(
+                        (chain_id, sequence_number), (target_id, target_seq)
+                    )
+
+        db_pool.simple_insert_many_txn(
+            txn,
+            table="event_auth_chain_links",
+            values=[
+                {
+                    "origin_chain_id": source_id,
+                    "origin_sequence_number": source_seq,
+                    "target_chain_id": target_id,
+                    "target_sequence_number": target_seq,
+                }
+                for (
+                    source_id,
+                    source_seq,
+                    target_id,
+                    target_seq,
+                ) in chain_links.get_additions()
+            ],
+        )
+
+    @staticmethod
+    def _allocate_chain_ids(
+        txn,
+        db_pool: DatabasePool,
+        event_to_room_id: Dict[str, str],
+        event_to_types: Dict[str, Tuple[str, str]],
+        event_to_auth_chain: Dict[str, List[str]],
+        events_to_calc_chain_id_for: Set[str],
+        chain_map: Dict[str, Tuple[int, int]],
+    ) -> Dict[str, Tuple[int, int]]:
+        """Allocates, but does not persist, chain ID/sequence numbers for the
+        events in `events_to_calc_chain_id_for`. (c.f. _add_chain_cover_index
+        for info on args)
+        """
+
+        # We now calculate the chain IDs/sequence numbers for the events. We do
+        # this by looking at the chain ID and sequence number of any auth event
+        # with the same type/state_key and incrementing the sequence number by
+        # one. If there was no match or the chain ID/sequence number is already
+        # taken we generate a new chain.
+        #
+        # We try to reduce the number of times that we hit the database by
+        # batching up calls, to make this more efficient when persisting large
+        # numbers of state events (e.g. during joins).
+        #
+        # We do this by:
+        #   1. Calculating for each event which auth event will be used to
+        #      inherit the chain ID, i.e. converting the auth chain graph to a
+        #      tree that we can allocate chains on. We also keep track of which
+        #      existing chain IDs have been referenced.
+        #   2. Fetching the max allocated sequence number for each referenced
+        #      existing chain ID, generating a map from chain ID to the max
+        #      allocated sequence number.
+        #   3. Iterating over the tree and allocating a chain ID/seq no. to the
+        #      new event, by incrementing the sequence number from the
+        #      referenced event's chain ID/seq no. and checking that the
+        #      incremented sequence number hasn't already been allocated (by
+        #      looking in the map generated in the previous step). We generate a
+        #      new chain if the sequence number has already been allocated.
+        #
+
+        existing_chains = set()  # type: Set[int]
+        tree = []  # type: List[Tuple[str, Optional[str]]]
+
+        # We need to do this in a topologically sorted order as we want to
+        # generate chain IDs/sequence numbers of an event's auth events before
+        # the event itself.
+        for event_id in sorted_topologically(
+            events_to_calc_chain_id_for, event_to_auth_chain
+        ):
+            for auth_id in event_to_auth_chain.get(event_id, []):
+                if event_to_types.get(event_id) == event_to_types.get(auth_id):
+                    existing_chain_id = chain_map.get(auth_id)
+                    if existing_chain_id:
+                        existing_chains.add(existing_chain_id[0])
+
+                    tree.append((event_id, auth_id))
+                    break
+            else:
+                tree.append((event_id, None))
+
+        # Fetch the current max sequence number for each existing referenced chain.
+        sql = """
+            SELECT chain_id, MAX(sequence_number) FROM event_auth_chains
+            WHERE %s
+            GROUP BY chain_id
+        """
+        clause, args = make_in_list_sql_clause(
+            db_pool.engine, "chain_id", existing_chains
+        )
+        txn.execute(sql % (clause,), args)
+
+        chain_to_max_seq_no = {row[0]: row[1] for row in txn}  # type: Dict[Any, int]
+
+        # Allocate the new events chain ID/sequence numbers.
+        #
+        # To reduce the number of calls to the database we don't allocate a
+        # chain ID number in the loop, instead we use a temporary `object()` for
+        # each new chain ID. Once we've done the loop we generate the necessary
+        # number of new chain IDs in one call, replacing all temporary
+        # objects with real allocated chain IDs.
+
+        unallocated_chain_ids = set()  # type: Set[object]
+        new_chain_tuples = {}  # type: Dict[str, Tuple[Any, int]]
+        for event_id, auth_event_id in tree:
+            # If we reference an auth_event_id we fetch the allocated chain ID,
+            # either from the existing `chain_map` or the newly generated
+            # `new_chain_tuples` map.
+            existing_chain_id = None
+            if auth_event_id:
+                existing_chain_id = new_chain_tuples.get(auth_event_id)
+                if not existing_chain_id:
+                    existing_chain_id = chain_map[auth_event_id]
+
+            new_chain_tuple = None  # type: Optional[Tuple[Any, int]]
+            if existing_chain_id:
+                # We found a chain ID/sequence number candidate, check its
+                # not already taken.
+                proposed_new_id = existing_chain_id[0]
+                proposed_new_seq = existing_chain_id[1] + 1
+
+                if chain_to_max_seq_no[proposed_new_id] < proposed_new_seq:
+                    new_chain_tuple = (
+                        proposed_new_id,
+                        proposed_new_seq,
+                    )
+
+            # If we need to start a new chain we allocate a temporary chain ID.
+            if not new_chain_tuple:
+                new_chain_tuple = (object(), 1)
+                unallocated_chain_ids.add(new_chain_tuple[0])
+
+            new_chain_tuples[event_id] = new_chain_tuple
+            chain_to_max_seq_no[new_chain_tuple[0]] = new_chain_tuple[1]
+
+        # Generate new chain IDs for all unallocated chain IDs.
+        newly_allocated_chain_ids = db_pool.event_chain_id_gen.get_next_mult_txn(
+            txn, len(unallocated_chain_ids)
+        )
+
+        # Map from potentially temporary chain ID to real chain ID
+        chain_id_to_allocated_map = dict(
+            zip(unallocated_chain_ids, newly_allocated_chain_ids)
+        )  # type: Dict[Any, int]
+        chain_id_to_allocated_map.update((c, c) for c in existing_chains)
+
+        return {
+            event_id: (chain_id_to_allocated_map[chain_id], seq)
+            for event_id, (chain_id, seq) in new_chain_tuples.items()
+        }
 
     def _persist_transaction_ids_txn(
         self,
@@ -489,7 +965,7 @@ class PersistEventsStore:
                         WHERE room_id = ? AND type = ? AND state_key = ?
                     )
                 """
-                txn.executemany(
+                txn.execute_batch(
                     sql,
                     (
                         (
@@ -508,7 +984,7 @@ class PersistEventsStore:
                 )
                 # Now we actually update the current_state_events table
 
-                txn.executemany(
+                txn.execute_batch(
                     "DELETE FROM current_state_events"
                     " WHERE room_id = ? AND type = ? AND state_key = ?",
                     (
@@ -520,7 +996,7 @@ class PersistEventsStore:
                 # We include the membership in the current state table, hence we do
                 # a lookup when we insert. This assumes that all events have already
                 # been inserted into room_memberships.
-                txn.executemany(
+                txn.execute_batch(
                     """INSERT INTO current_state_events
                         (room_id, type, state_key, event_id, membership)
                     VALUES (?, ?, ?, ?, (SELECT membership FROM room_memberships WHERE event_id = ?))
@@ -540,7 +1016,7 @@ class PersistEventsStore:
             # we have no record of the fact the user *was* a member of the
             # room but got, say, state reset out of it.
             if to_delete or to_insert:
-                txn.executemany(
+                txn.execute_batch(
                     "DELETE FROM local_current_membership"
                     " WHERE room_id = ? AND user_id = ?",
                     (
@@ -551,7 +1027,7 @@ class PersistEventsStore:
                 )
 
             if to_insert:
-                txn.executemany(
+                txn.execute_batch(
                     """INSERT INTO local_current_membership
                         (room_id, user_id, event_id, membership)
                     VALUES (?, ?, ?, (SELECT membership FROM room_memberships WHERE event_id = ?))
@@ -799,7 +1275,8 @@ class PersistEventsStore:
         return [ec for ec in events_and_contexts if ec[0] not in to_remove]
 
     def _store_event_txn(self, txn, events_and_contexts):
-        """Insert new events into the event and event_json tables
+        """Insert new events into the event, event_json, redaction and
+        state_events tables.
 
         Args:
             txn (twisted.enterprise.adbapi.Connection): db connection
@@ -871,6 +1348,29 @@ class PersistEventsStore:
                     updatevalues={"have_censored": False},
                 )
 
+        state_events_and_contexts = [
+            ec for ec in events_and_contexts if ec[0].is_state()
+        ]
+
+        state_values = []
+        for event, context in state_events_and_contexts:
+            vals = {
+                "event_id": event.event_id,
+                "room_id": event.room_id,
+                "type": event.type,
+                "state_key": event.state_key,
+            }
+
+            # TODO: How does this work with backfilling?
+            if hasattr(event, "replaces_state"):
+                vals["prev_state"] = event.replaces_state
+
+            state_values.append(vals)
+
+        self.db_pool.simple_insert_many_txn(
+            txn, table="state_events", values=state_values
+        )
+
     def _store_rejected_events_txn(self, txn, events_and_contexts):
         """Add rows to the 'rejections' table for received events which were
         rejected
@@ -987,29 +1487,6 @@ class PersistEventsStore:
             txn, [event for event, _ in events_and_contexts]
         )
 
-        state_events_and_contexts = [
-            ec for ec in events_and_contexts if ec[0].is_state()
-        ]
-
-        state_values = []
-        for event, context in state_events_and_contexts:
-            vals = {
-                "event_id": event.event_id,
-                "room_id": event.room_id,
-                "type": event.type,
-                "state_key": event.state_key,
-            }
-
-            # TODO: How does this work with backfilling?
-            if hasattr(event, "replaces_state"):
-                vals["prev_state"] = event.replaces_state
-
-            state_values.append(vals)
-
-        self.db_pool.simple_insert_many_txn(
-            txn, table="state_events", values=state_values
-        )
-
         # Prefill the event cache
         self._add_to_cache(txn, events_and_contexts)
 
@@ -1350,7 +1827,7 @@ class PersistEventsStore:
         """
 
         if events_and_contexts:
-            txn.executemany(
+            txn.execute_batch(
                 sql,
                 (
                     (
@@ -1379,7 +1856,7 @@ class PersistEventsStore:
 
         # Now we delete the staging area for *all* events that were being
         # persisted.
-        txn.executemany(
+        txn.execute_batch(
             "DELETE FROM event_push_actions_staging WHERE event_id = ?",
             ((event.event_id,) for event, _ in all_events_and_contexts),
         )
@@ -1498,7 +1975,7 @@ class PersistEventsStore:
             " )"
         )
 
-        txn.executemany(
+        txn.execute_batch(
             query,
             [
                 (e_id, ev.room_id, e_id, ev.room_id, e_id, ev.room_id, False)
@@ -1512,7 +1989,7 @@ class PersistEventsStore:
             "DELETE FROM event_backward_extremities"
             " WHERE event_id = ? AND room_id = ?"
         )
-        txn.executemany(
+        txn.execute_batch(
             query,
             [
                 (ev.event_id, ev.room_id)
@@ -1520,3 +1997,131 @@ class PersistEventsStore:
                 if not ev.internal_metadata.is_outlier()
             ],
         )
+
+
+@attr.s(slots=True)
+class _LinkMap:
+    """A helper type for tracking links between chains.
+    """
+
+    # Stores the set of links as nested maps: source chain ID -> target chain ID
+    # -> source sequence number -> target sequence number.
+    maps = attr.ib(type=Dict[int, Dict[int, Dict[int, int]]], factory=dict)
+
+    # Stores the links that have been added (with new set to true), as tuples of
+    # `(source chain ID, source sequence no, target chain ID, target sequence no.)`
+    additions = attr.ib(type=Set[Tuple[int, int, int, int]], factory=set)
+
+    def add_link(
+        self,
+        src_tuple: Tuple[int, int],
+        target_tuple: Tuple[int, int],
+        new: bool = True,
+    ) -> bool:
+        """Add a new link between two chains, ensuring no redundant links are added.
+
+        New links should be added in topological order.
+
+        Args:
+            src_tuple: The chain ID/sequence number of the source of the link.
+            target_tuple: The chain ID/sequence number of the target of the link.
+            new: Whether this is a "new" link, i.e. should it be returned
+                by `get_additions`.
+
+        Returns:
+            True if a link was added, false if the given link was dropped as redundant
+        """
+        src_chain, src_seq = src_tuple
+        target_chain, target_seq = target_tuple
+
+        current_links = self.maps.setdefault(src_chain, {}).setdefault(target_chain, {})
+
+        assert src_chain != target_chain
+
+        if new:
+            # Check if the new link is redundant
+            for current_seq_src, current_seq_target in current_links.items():
+                # If a link "crosses" another link then its redundant. For example
+                # in the following link 1 (L1) is redundant, as any event reachable
+                # via L1 is *also* reachable via L2.
+                #
+                #   Chain A     Chain B
+                #      |          |
+                #   L1 |------    |
+                #      |     |    |
+                #   L2 |---- | -->|
+                #      |     |    |
+                #      |     |--->|
+                #      |          |
+                #      |          |
+                #
+                # So we only need to keep links which *do not* cross, i.e. links
+                # that both start and end above or below an existing link.
+                #
+                # Note, since we add links in topological ordering we should never
+                # see `src_seq` less than `current_seq_src`.
+
+                if current_seq_src <= src_seq and target_seq <= current_seq_target:
+                    # This new link is redundant, nothing to do.
+                    return False
+
+            self.additions.add((src_chain, src_seq, target_chain, target_seq))
+
+        current_links[src_seq] = target_seq
+        return True
+
+    def get_links_from(
+        self, src_tuple: Tuple[int, int]
+    ) -> Generator[Tuple[int, int], None, None]:
+        """Gets the chains reachable from the given chain/sequence number.
+
+        Yields:
+            The chain ID and sequence number the link points to.
+        """
+        src_chain, src_seq = src_tuple
+        for target_id, sequence_numbers in self.maps.get(src_chain, {}).items():
+            for link_src_seq, target_seq in sequence_numbers.items():
+                if link_src_seq <= src_seq:
+                    yield target_id, target_seq
+
+    def get_links_between(
+        self, source_chain: int, target_chain: int
+    ) -> Generator[Tuple[int, int], None, None]:
+        """Gets the links between two chains.
+
+        Yields:
+            The source and target sequence numbers.
+        """
+
+        yield from self.maps.get(source_chain, {}).get(target_chain, {}).items()
+
+    def get_additions(self) -> Generator[Tuple[int, int, int, int], None, None]:
+        """Gets any newly added links.
+
+        Yields:
+            The source chain ID/sequence number and target chain ID/sequence number
+        """
+
+        for src_chain, src_seq, target_chain, _ in self.additions:
+            target_seq = self.maps.get(src_chain, {}).get(target_chain, {}).get(src_seq)
+            if target_seq is not None:
+                yield (src_chain, src_seq, target_chain, target_seq)
+
+    def exists_path_from(
+        self, src_tuple: Tuple[int, int], target_tuple: Tuple[int, int],
+    ) -> bool:
+        """Checks if there is a path between the source chain ID/sequence and
+        target chain ID/sequence.
+        """
+        src_chain, src_seq = src_tuple
+        target_chain, target_seq = target_tuple
+
+        if src_chain == target_chain:
+            return target_seq <= src_seq
+
+        links = self.get_links_between(src_chain, target_chain)
+        for link_start_seq, link_end_seq in links:
+            if link_start_seq <= src_seq and target_seq <= link_end_seq:
+                return True
+
+        return False
diff --git a/synapse/storage/databases/main/events_bg_updates.py b/synapse/storage/databases/main/events_bg_updates.py
index 97b6754846..5ca4fa6817 100644
--- a/synapse/storage/databases/main/events_bg_updates.py
+++ b/synapse/storage/databases/main/events_bg_updates.py
@@ -14,14 +14,41 @@
 # limitations under the License.
 
 import logging
+from typing import Dict, List, Optional, Tuple
+
+import attr
 
 from synapse.api.constants import EventContentFields
+from synapse.api.room_versions import KNOWN_ROOM_VERSIONS
+from synapse.events import make_event_from_dict
 from synapse.storage._base import SQLBaseStore, db_to_json, make_in_list_sql_clause
-from synapse.storage.database import DatabasePool
+from synapse.storage.database import DatabasePool, make_tuple_comparison_clause
+from synapse.storage.databases.main.events import PersistEventsStore
+from synapse.storage.types import Cursor
+from synapse.types import JsonDict
 
 logger = logging.getLogger(__name__)
 
 
+@attr.s(slots=True, frozen=True)
+class _CalculateChainCover:
+    """Return value for _calculate_chain_cover_txn.
+    """
+
+    # The last room_id/depth/stream processed.
+    room_id = attr.ib(type=str)
+    depth = attr.ib(type=int)
+    stream = attr.ib(type=int)
+
+    # Number of rows processed
+    processed_count = attr.ib(type=int)
+
+    # Map from room_id to last depth/stream processed for each room that we have
+    # processed all events for (i.e. the rooms we can flip the
+    # `has_auth_chain_index` for)
+    finished_room_map = attr.ib(type=Dict[str, Tuple[int, int]])
+
+
 class EventsBackgroundUpdatesStore(SQLBaseStore):
 
     EVENT_ORIGIN_SERVER_TS_NAME = "event_origin_server_ts"
@@ -99,13 +126,19 @@ class EventsBackgroundUpdatesStore(SQLBaseStore):
             columns=["user_id", "created_ts"],
         )
 
+        self.db_pool.updates.register_background_update_handler(
+            "rejected_events_metadata", self._rejected_events_metadata,
+        )
+
+        self.db_pool.updates.register_background_update_handler(
+            "chain_cover", self._chain_cover_index,
+        )
+
     async def _background_reindex_fields_sender(self, progress, batch_size):
         target_min_stream_id = progress["target_min_stream_id_inclusive"]
         max_stream_id = progress["max_stream_id_exclusive"]
         rows_inserted = progress.get("rows_inserted", 0)
 
-        INSERT_CLUMP_SIZE = 1000
-
         def reindex_txn(txn):
             sql = (
                 "SELECT stream_ordering, event_id, json FROM events"
@@ -143,9 +176,7 @@ class EventsBackgroundUpdatesStore(SQLBaseStore):
 
             sql = "UPDATE events SET sender = ?, contains_url = ? WHERE event_id = ?"
 
-            for index in range(0, len(update_rows), INSERT_CLUMP_SIZE):
-                clump = update_rows[index : index + INSERT_CLUMP_SIZE]
-                txn.executemany(sql, clump)
+            txn.execute_batch(sql, update_rows)
 
             progress = {
                 "target_min_stream_id_inclusive": target_min_stream_id,
@@ -175,8 +206,6 @@ class EventsBackgroundUpdatesStore(SQLBaseStore):
         max_stream_id = progress["max_stream_id_exclusive"]
         rows_inserted = progress.get("rows_inserted", 0)
 
-        INSERT_CLUMP_SIZE = 1000
-
         def reindex_search_txn(txn):
             sql = (
                 "SELECT stream_ordering, event_id FROM events"
@@ -221,9 +250,7 @@ class EventsBackgroundUpdatesStore(SQLBaseStore):
 
             sql = "UPDATE events SET origin_server_ts = ? WHERE event_id = ?"
 
-            for index in range(0, len(rows_to_update), INSERT_CLUMP_SIZE):
-                clump = rows_to_update[index : index + INSERT_CLUMP_SIZE]
-                txn.executemany(sql, clump)
+            txn.execute_batch(sql, rows_to_update)
 
             progress = {
                 "target_min_stream_id_inclusive": target_min_stream_id,
@@ -582,3 +609,314 @@ class EventsBackgroundUpdatesStore(SQLBaseStore):
             await self.db_pool.updates._end_background_update("event_store_labels")
 
         return num_rows
+
+    async def _rejected_events_metadata(self, progress: dict, batch_size: int) -> int:
+        """Adds rejected events to the `state_events` and `event_auth` metadata
+        tables.
+        """
+
+        last_event_id = progress.get("last_event_id", "")
+
+        def get_rejected_events(
+            txn: Cursor,
+        ) -> List[Tuple[str, str, JsonDict, bool, bool]]:
+            # Fetch rejected event json, their room version and whether we have
+            # inserted them into the state_events or auth_events tables.
+            #
+            # Note we can assume that events that don't have a corresponding
+            # room version are V1 rooms.
+            sql = """
+                SELECT DISTINCT
+                    event_id,
+                    COALESCE(room_version, '1'),
+                    json,
+                    state_events.event_id IS NOT NULL,
+                    event_auth.event_id IS NOT NULL
+                FROM rejections
+                INNER JOIN event_json USING (event_id)
+                LEFT JOIN rooms USING (room_id)
+                LEFT JOIN state_events USING (event_id)
+                LEFT JOIN event_auth USING (event_id)
+                WHERE event_id > ?
+                ORDER BY event_id
+                LIMIT ?
+            """
+
+            txn.execute(sql, (last_event_id, batch_size,))
+
+            return [(row[0], row[1], db_to_json(row[2]), row[3], row[4]) for row in txn]  # type: ignore
+
+        results = await self.db_pool.runInteraction(
+            desc="_rejected_events_metadata_get", func=get_rejected_events
+        )
+
+        if not results:
+            await self.db_pool.updates._end_background_update(
+                "rejected_events_metadata"
+            )
+            return 0
+
+        state_events = []
+        auth_events = []
+        for event_id, room_version, event_json, has_state, has_event_auth in results:
+            last_event_id = event_id
+
+            if has_state and has_event_auth:
+                continue
+
+            room_version_obj = KNOWN_ROOM_VERSIONS.get(room_version)
+            if not room_version_obj:
+                # We no longer support this room version, so we just ignore the
+                # events entirely.
+                logger.info(
+                    "Ignoring event with unknown room version %r: %r",
+                    room_version,
+                    event_id,
+                )
+                continue
+
+            event = make_event_from_dict(event_json, room_version_obj)
+
+            if not event.is_state():
+                continue
+
+            if not has_state:
+                state_events.append(
+                    {
+                        "event_id": event.event_id,
+                        "room_id": event.room_id,
+                        "type": event.type,
+                        "state_key": event.state_key,
+                    }
+                )
+
+            if not has_event_auth:
+                for auth_id in event.auth_event_ids():
+                    auth_events.append(
+                        {
+                            "room_id": event.room_id,
+                            "event_id": event.event_id,
+                            "auth_id": auth_id,
+                        }
+                    )
+
+        if state_events:
+            await self.db_pool.simple_insert_many(
+                table="state_events",
+                values=state_events,
+                desc="_rejected_events_metadata_state_events",
+            )
+
+        if auth_events:
+            await self.db_pool.simple_insert_many(
+                table="event_auth",
+                values=auth_events,
+                desc="_rejected_events_metadata_event_auth",
+            )
+
+        await self.db_pool.updates._background_update_progress(
+            "rejected_events_metadata", {"last_event_id": last_event_id}
+        )
+
+        if len(results) < batch_size:
+            await self.db_pool.updates._end_background_update(
+                "rejected_events_metadata"
+            )
+
+        return len(results)
+
+    async def _chain_cover_index(self, progress: dict, batch_size: int) -> int:
+        """A background updates that iterates over all rooms and generates the
+        chain cover index for them.
+        """
+
+        current_room_id = progress.get("current_room_id", "")
+
+        # Where we've processed up to in the room, defaults to the start of the
+        # room.
+        last_depth = progress.get("last_depth", -1)
+        last_stream = progress.get("last_stream", -1)
+
+        result = await self.db_pool.runInteraction(
+            "_chain_cover_index",
+            self._calculate_chain_cover_txn,
+            current_room_id,
+            last_depth,
+            last_stream,
+            batch_size,
+            single_room=False,
+        )
+
+        finished = result.processed_count == 0
+
+        total_rows_processed = result.processed_count
+        current_room_id = result.room_id
+        last_depth = result.depth
+        last_stream = result.stream
+
+        for room_id, (depth, stream) in result.finished_room_map.items():
+            # If we've done all the events in the room we flip the
+            # `has_auth_chain_index` in the DB. Note that its possible for
+            # further events to be persisted between the above and setting the
+            # flag without having the chain cover calculated for them. This is
+            # fine as a) the code gracefully handles these cases and b) we'll
+            # calculate them below.
+
+            await self.db_pool.simple_update(
+                table="rooms",
+                keyvalues={"room_id": room_id},
+                updatevalues={"has_auth_chain_index": True},
+                desc="_chain_cover_index",
+            )
+
+            # Handle any events that might have raced with us flipping the
+            # bit above.
+            result = await self.db_pool.runInteraction(
+                "_chain_cover_index",
+                self._calculate_chain_cover_txn,
+                room_id,
+                depth,
+                stream,
+                batch_size=None,
+                single_room=True,
+            )
+
+            total_rows_processed += result.processed_count
+
+        if finished:
+            await self.db_pool.updates._end_background_update("chain_cover")
+            return total_rows_processed
+
+        await self.db_pool.updates._background_update_progress(
+            "chain_cover",
+            {
+                "current_room_id": current_room_id,
+                "last_depth": last_depth,
+                "last_stream": last_stream,
+            },
+        )
+
+        return total_rows_processed
+
+    def _calculate_chain_cover_txn(
+        self,
+        txn: Cursor,
+        last_room_id: str,
+        last_depth: int,
+        last_stream: int,
+        batch_size: Optional[int],
+        single_room: bool,
+    ) -> _CalculateChainCover:
+        """Calculate the chain cover for `batch_size` events, ordered by
+        `(room_id, depth, stream)`.
+
+        Args:
+            txn,
+            last_room_id, last_depth, last_stream: The `(room_id, depth, stream)`
+                tuple to fetch results after.
+            batch_size: The maximum number of events to process. If None then
+                no limit.
+            single_room: Whether to calculate the index for just the given
+                room.
+        """
+
+        # Get the next set of events in the room (that we haven't already
+        # computed chain cover for). We do this in topological order.
+
+        # We want to do a `(topological_ordering, stream_ordering) > (?,?)`
+        # comparison, but that is not supported on older SQLite versions
+        tuple_clause, tuple_args = make_tuple_comparison_clause(
+            self.database_engine,
+            [
+                ("events.room_id", last_room_id),
+                ("topological_ordering", last_depth),
+                ("stream_ordering", last_stream),
+            ],
+        )
+
+        extra_clause = ""
+        if single_room:
+            extra_clause = "AND events.room_id = ?"
+            tuple_args.append(last_room_id)
+
+        sql = """
+            SELECT
+                event_id, state_events.type, state_events.state_key,
+                topological_ordering, stream_ordering,
+                events.room_id
+            FROM events
+            INNER JOIN state_events USING (event_id)
+            LEFT JOIN event_auth_chains USING (event_id)
+            LEFT JOIN event_auth_chain_to_calculate USING (event_id)
+            WHERE event_auth_chains.event_id IS NULL
+                AND event_auth_chain_to_calculate.event_id IS NULL
+                AND %(tuple_cmp)s
+                %(extra)s
+            ORDER BY events.room_id, topological_ordering, stream_ordering
+            %(limit)s
+        """ % {
+            "tuple_cmp": tuple_clause,
+            "limit": "LIMIT ?" if batch_size is not None else "",
+            "extra": extra_clause,
+        }
+
+        if batch_size is not None:
+            tuple_args.append(batch_size)
+
+        txn.execute(sql, tuple_args)
+        rows = txn.fetchall()
+
+        # Put the results in the necessary format for
+        # `_add_chain_cover_index`
+        event_to_room_id = {row[0]: row[5] for row in rows}
+        event_to_types = {row[0]: (row[1], row[2]) for row in rows}
+
+        # Calculate the new last position we've processed up to.
+        new_last_depth = rows[-1][3] if rows else last_depth  # type: int
+        new_last_stream = rows[-1][4] if rows else last_stream  # type: int
+        new_last_room_id = rows[-1][5] if rows else ""  # type: str
+
+        # Map from room_id to last depth/stream_ordering processed for the room,
+        # excluding the last room (which we're likely still processing). We also
+        # need to include the room passed in if it's not included in the result
+        # set (as we then know we've processed all events in said room).
+        #
+        # This is the set of rooms that we can now safely flip the
+        # `has_auth_chain_index` bit for.
+        finished_rooms = {
+            row[5]: (row[3], row[4]) for row in rows if row[5] != new_last_room_id
+        }
+        if last_room_id not in finished_rooms and last_room_id != new_last_room_id:
+            finished_rooms[last_room_id] = (last_depth, last_stream)
+
+        count = len(rows)
+
+        # We also need to fetch the auth events for them.
+        auth_events = self.db_pool.simple_select_many_txn(
+            txn,
+            table="event_auth",
+            column="event_id",
+            iterable=event_to_room_id,
+            keyvalues={},
+            retcols=("event_id", "auth_id"),
+        )
+
+        event_to_auth_chain = {}  # type: Dict[str, List[str]]
+        for row in auth_events:
+            event_to_auth_chain.setdefault(row["event_id"], []).append(row["auth_id"])
+
+        # Calculate and persist the chain cover index for this set of events.
+        #
+        # Annoyingly we need to gut wrench into the persit event store so that
+        # we can reuse the function to calculate the chain cover for rooms.
+        PersistEventsStore._add_chain_cover_index(
+            txn, self.db_pool, event_to_room_id, event_to_types, event_to_auth_chain,
+        )
+
+        return _CalculateChainCover(
+            room_id=new_last_room_id,
+            depth=new_last_depth,
+            stream=new_last_stream,
+            processed_count=count,
+            finished_room_map=finished_rooms,
+        )
diff --git a/synapse/storage/databases/main/events_worker.py b/synapse/storage/databases/main/events_worker.py
index 4732685f6e..71d823be72 100644
--- a/synapse/storage/databases/main/events_worker.py
+++ b/synapse/storage/databases/main/events_worker.py
@@ -96,9 +96,7 @@ class EventsWorkerStore(SQLBaseStore):
                 db=database,
                 stream_name="events",
                 instance_name=hs.get_instance_name(),
-                table="events",
-                instance_column="instance_name",
-                id_column="stream_ordering",
+                tables=[("events", "instance_name", "stream_ordering")],
                 sequence_name="events_stream_seq",
                 writers=hs.config.worker.writers.events,
             )
@@ -107,9 +105,7 @@ class EventsWorkerStore(SQLBaseStore):
                 db=database,
                 stream_name="backfill",
                 instance_name=hs.get_instance_name(),
-                table="events",
-                instance_column="instance_name",
-                id_column="stream_ordering",
+                tables=[("events", "instance_name", "stream_ordering")],
                 sequence_name="events_backfill_stream_seq",
                 positive=False,
                 writers=hs.config.worker.writers.events,
diff --git a/synapse/storage/databases/main/media_repository.py b/synapse/storage/databases/main/media_repository.py
index 4b2f224718..e017177655 100644
--- a/synapse/storage/databases/main/media_repository.py
+++ b/synapse/storage/databases/main/media_repository.py
@@ -1,5 +1,6 @@
 # -*- coding: utf-8 -*-
 # Copyright 2014-2016 OpenMarket Ltd
+# Copyright 2020-2021 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.
@@ -169,7 +170,7 @@ class MediaRepositoryStore(MediaRepositoryBackgroundUpdateStore):
 
     async def get_local_media_before(
         self, before_ts: int, size_gt: int, keep_profiles: bool,
-    ) -> Optional[List[str]]:
+    ) -> List[str]:
 
         # to find files that have never been accessed (last_access_ts IS NULL)
         # compare with `created_ts`
@@ -416,7 +417,7 @@ class MediaRepositoryStore(MediaRepositoryBackgroundUpdateStore):
                 " WHERE media_origin = ? AND media_id = ?"
             )
 
-            txn.executemany(
+            txn.execute_batch(
                 sql,
                 (
                     (time_ms, media_origin, media_id)
@@ -429,7 +430,7 @@ class MediaRepositoryStore(MediaRepositoryBackgroundUpdateStore):
                 " WHERE media_id = ?"
             )
 
-            txn.executemany(sql, ((time_ms, media_id) for media_id in local_media))
+            txn.execute_batch(sql, ((time_ms, media_id) for media_id in local_media))
 
         return await self.db_pool.runInteraction(
             "update_cached_last_access_time", update_cache_txn
@@ -556,7 +557,7 @@ class MediaRepositoryStore(MediaRepositoryBackgroundUpdateStore):
         sql = "DELETE FROM local_media_repository_url_cache WHERE media_id = ?"
 
         def _delete_url_cache_txn(txn):
-            txn.executemany(sql, [(media_id,) for media_id in media_ids])
+            txn.execute_batch(sql, [(media_id,) for media_id in media_ids])
 
         return await self.db_pool.runInteraction(
             "delete_url_cache", _delete_url_cache_txn
@@ -585,11 +586,11 @@ class MediaRepositoryStore(MediaRepositoryBackgroundUpdateStore):
         def _delete_url_cache_media_txn(txn):
             sql = "DELETE FROM local_media_repository WHERE media_id = ?"
 
-            txn.executemany(sql, [(media_id,) for media_id in media_ids])
+            txn.execute_batch(sql, [(media_id,) for media_id in media_ids])
 
             sql = "DELETE FROM local_media_repository_thumbnails WHERE media_id = ?"
 
-            txn.executemany(sql, [(media_id,) for media_id in media_ids])
+            txn.execute_batch(sql, [(media_id,) for media_id in media_ids])
 
         return await self.db_pool.runInteraction(
             "delete_url_cache_media", _delete_url_cache_media_txn
diff --git a/synapse/storage/databases/main/profile.py b/synapse/storage/databases/main/profile.py
index 0e25ca3d7a..54ef0f1f54 100644
--- a/synapse/storage/databases/main/profile.py
+++ b/synapse/storage/databases/main/profile.py
@@ -82,7 +82,7 @@ class ProfileWorkerStore(SQLBaseStore):
         )
 
     async def set_profile_avatar_url(
-        self, user_localpart: str, new_avatar_url: str
+        self, user_localpart: str, new_avatar_url: Optional[str]
     ) -> None:
         await self.db_pool.simple_update_one(
             table="profiles",
diff --git a/synapse/storage/databases/main/purge_events.py b/synapse/storage/databases/main/purge_events.py
index 5d668aadb2..ecfc9f20b1 100644
--- a/synapse/storage/databases/main/purge_events.py
+++ b/synapse/storage/databases/main/purge_events.py
@@ -172,7 +172,7 @@ class PurgeEventsStore(StateGroupWorkerStore, SQLBaseStore):
         )
 
         # Update backward extremeties
-        txn.executemany(
+        txn.execute_batch(
             "INSERT INTO event_backward_extremities (room_id, event_id)"
             " VALUES (?, ?)",
             [(room_id, event_id) for event_id, in new_backwards_extrems],
diff --git a/synapse/storage/databases/main/pusher.py b/synapse/storage/databases/main/pusher.py
index 77ba9d819e..bc7621b8d6 100644
--- a/synapse/storage/databases/main/pusher.py
+++ b/synapse/storage/databases/main/pusher.py
@@ -17,14 +17,13 @@
 import logging
 from typing import TYPE_CHECKING, Any, Dict, Iterable, Iterator, List, Optional, Tuple
 
-from canonicaljson import encode_canonical_json
-
 from synapse.push import PusherConfig, ThrottleParams
 from synapse.storage._base import SQLBaseStore, db_to_json
 from synapse.storage.database import DatabasePool
 from synapse.storage.types import Connection
 from synapse.storage.util.id_generators import StreamIdGenerator
 from synapse.types import JsonDict
+from synapse.util import json_encoder
 from synapse.util.caches.descriptors import cached, cachedList
 
 if TYPE_CHECKING:
@@ -315,7 +314,7 @@ class PusherStore(PusherWorkerStore):
                     "device_display_name": device_display_name,
                     "ts": pushkey_ts,
                     "lang": lang,
-                    "data": bytearray(encode_canonical_json(data)),
+                    "data": json_encoder.encode(data),
                     "last_stream_ordering": last_stream_ordering,
                     "profile_tag": profile_tag,
                     "id": stream_id,
diff --git a/synapse/storage/databases/main/receipts.py b/synapse/storage/databases/main/receipts.py
index 1e7949a323..e4843a202c 100644
--- a/synapse/storage/databases/main/receipts.py
+++ b/synapse/storage/databases/main/receipts.py
@@ -14,15 +14,17 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
-import abc
 import logging
 from typing import Any, Dict, List, Optional, Tuple
 
 from twisted.internet import defer
 
+from synapse.replication.slave.storage._slaved_id_tracker import SlavedIdTracker
+from synapse.replication.tcp.streams import ReceiptsStream
 from synapse.storage._base import SQLBaseStore, db_to_json, make_in_list_sql_clause
 from synapse.storage.database import DatabasePool
-from synapse.storage.util.id_generators import StreamIdGenerator
+from synapse.storage.engines import PostgresEngine
+from synapse.storage.util.id_generators import MultiWriterIdGenerator, StreamIdGenerator
 from synapse.types import JsonDict
 from synapse.util import json_encoder
 from synapse.util.caches.descriptors import cached, cachedList
@@ -31,28 +33,56 @@ from synapse.util.caches.stream_change_cache import StreamChangeCache
 logger = logging.getLogger(__name__)
 
 
-# The ABCMeta metaclass ensures that it cannot be instantiated without
-# the abstract methods being implemented.
-class ReceiptsWorkerStore(SQLBaseStore, metaclass=abc.ABCMeta):
-    """This is an abstract base class where subclasses must implement
-    `get_max_receipt_stream_id` which can be called in the initializer.
-    """
-
+class ReceiptsWorkerStore(SQLBaseStore):
     def __init__(self, database: DatabasePool, db_conn, hs):
+        self._instance_name = hs.get_instance_name()
+
+        if isinstance(database.engine, PostgresEngine):
+            self._can_write_to_receipts = (
+                self._instance_name in hs.config.worker.writers.receipts
+            )
+
+            self._receipts_id_gen = MultiWriterIdGenerator(
+                db_conn=db_conn,
+                db=database,
+                stream_name="receipts",
+                instance_name=self._instance_name,
+                tables=[("receipts_linearized", "instance_name", "stream_id")],
+                sequence_name="receipts_sequence",
+                writers=hs.config.worker.writers.receipts,
+            )
+        else:
+            self._can_write_to_receipts = True
+
+            # We shouldn't be running in worker mode with SQLite, but its useful
+            # to support it for unit tests.
+            #
+            # If this process is the writer than we need to use
+            # `StreamIdGenerator`, otherwise we use `SlavedIdTracker` which gets
+            # updated over replication. (Multiple writers are not supported for
+            # SQLite).
+            if hs.get_instance_name() in hs.config.worker.writers.receipts:
+                self._receipts_id_gen = StreamIdGenerator(
+                    db_conn, "receipts_linearized", "stream_id"
+                )
+            else:
+                self._receipts_id_gen = SlavedIdTracker(
+                    db_conn, "receipts_linearized", "stream_id"
+                )
+
         super().__init__(database, db_conn, hs)
 
         self._receipts_stream_cache = StreamChangeCache(
             "ReceiptsRoomChangeCache", self.get_max_receipt_stream_id()
         )
 
-    @abc.abstractmethod
     def get_max_receipt_stream_id(self):
         """Get the current max stream ID for receipts stream
 
         Returns:
             int
         """
-        raise NotImplementedError()
+        return self._receipts_id_gen.get_current_token()
 
     @cached()
     async def get_users_with_read_receipts_in_room(self, room_id):
@@ -428,19 +458,25 @@ class ReceiptsWorkerStore(SQLBaseStore, metaclass=abc.ABCMeta):
 
         self.get_users_with_read_receipts_in_room.invalidate((room_id,))
 
-
-class ReceiptsStore(ReceiptsWorkerStore):
-    def __init__(self, database: DatabasePool, db_conn, hs):
-        # We instantiate this first as the ReceiptsWorkerStore constructor
-        # needs to be able to call get_max_receipt_stream_id
-        self._receipts_id_gen = StreamIdGenerator(
-            db_conn, "receipts_linearized", "stream_id"
+    def invalidate_caches_for_receipt(self, room_id, receipt_type, user_id):
+        self.get_receipts_for_user.invalidate((user_id, receipt_type))
+        self._get_linearized_receipts_for_room.invalidate_many((room_id,))
+        self.get_last_receipt_event_id_for_user.invalidate(
+            (user_id, room_id, receipt_type)
         )
+        self._invalidate_get_users_with_receipts_in_room(room_id, receipt_type, user_id)
+        self.get_receipts_for_room.invalidate((room_id, receipt_type))
+
+    def process_replication_rows(self, stream_name, instance_name, token, rows):
+        if stream_name == ReceiptsStream.NAME:
+            self._receipts_id_gen.advance(instance_name, token)
+            for row in rows:
+                self.invalidate_caches_for_receipt(
+                    row.room_id, row.receipt_type, row.user_id
+                )
+                self._receipts_stream_cache.entity_has_changed(row.room_id, token)
 
-        super().__init__(database, db_conn, hs)
-
-    def get_max_receipt_stream_id(self):
-        return self._receipts_id_gen.get_current_token()
+        return super().process_replication_rows(stream_name, instance_name, token, rows)
 
     def insert_linearized_receipt_txn(
         self, txn, room_id, receipt_type, user_id, event_id, data, stream_id
@@ -452,6 +488,8 @@ class ReceiptsStore(ReceiptsWorkerStore):
             otherwise, the rx timestamp of the event that the RR corresponds to
                 (or 0 if the event is unknown)
         """
+        assert self._can_write_to_receipts
+
         res = self.db_pool.simple_select_one_txn(
             txn,
             table="events",
@@ -483,28 +521,14 @@ class ReceiptsStore(ReceiptsWorkerStore):
                     )
                     return None
 
-        txn.call_after(self.get_receipts_for_room.invalidate, (room_id, receipt_type))
-        txn.call_after(
-            self._invalidate_get_users_with_receipts_in_room,
-            room_id,
-            receipt_type,
-            user_id,
-        )
-        txn.call_after(self.get_receipts_for_user.invalidate, (user_id, receipt_type))
-        # FIXME: This shouldn't invalidate the whole cache
         txn.call_after(
-            self._get_linearized_receipts_for_room.invalidate_many, (room_id,)
+            self.invalidate_caches_for_receipt, room_id, receipt_type, user_id
         )
 
         txn.call_after(
             self._receipts_stream_cache.entity_has_changed, room_id, stream_id
         )
 
-        txn.call_after(
-            self.get_last_receipt_event_id_for_user.invalidate,
-            (user_id, room_id, receipt_type),
-        )
-
         self.db_pool.simple_upsert_txn(
             txn,
             table="receipts_linearized",
@@ -543,6 +567,8 @@ class ReceiptsStore(ReceiptsWorkerStore):
         Automatically does conversion between linearized and graph
         representations.
         """
+        assert self._can_write_to_receipts
+
         if not event_ids:
             return None
 
@@ -607,6 +633,8 @@ class ReceiptsStore(ReceiptsWorkerStore):
     async def insert_graph_receipt(
         self, room_id, receipt_type, user_id, event_ids, data
     ):
+        assert self._can_write_to_receipts
+
         return await self.db_pool.runInteraction(
             "insert_graph_receipt",
             self.insert_graph_receipt_txn,
@@ -620,6 +648,8 @@ class ReceiptsStore(ReceiptsWorkerStore):
     def insert_graph_receipt_txn(
         self, txn, room_id, receipt_type, user_id, event_ids, data
     ):
+        assert self._can_write_to_receipts
+
         txn.call_after(self.get_receipts_for_room.invalidate, (room_id, receipt_type))
         txn.call_after(
             self._invalidate_get_users_with_receipts_in_room,
@@ -653,3 +683,7 @@ class ReceiptsStore(ReceiptsWorkerStore):
                 "data": json_encoder.encode(data),
             },
         )
+
+
+class ReceiptsStore(ReceiptsWorkerStore):
+    pass
diff --git a/synapse/storage/databases/main/registration.py b/synapse/storage/databases/main/registration.py
index 8d05288ed4..585b4049d6 100644
--- a/synapse/storage/databases/main/registration.py
+++ b/synapse/storage/databases/main/registration.py
@@ -1104,7 +1104,7 @@ class RegistrationBackgroundUpdateStore(RegistrationWorkerStore):
                 FROM user_threepids
             """
 
-            txn.executemany(sql, [(id_server,) for id_server in id_servers])
+            txn.execute_batch(sql, [(id_server,) for id_server in id_servers])
 
         if id_servers:
             await self.db_pool.runInteraction(
diff --git a/synapse/storage/databases/main/room.py b/synapse/storage/databases/main/room.py
index 4650d0689b..a9fcb5f59c 100644
--- a/synapse/storage/databases/main/room.py
+++ b/synapse/storage/databases/main/room.py
@@ -16,7 +16,6 @@
 
 import collections
 import logging
-import re
 from abc import abstractmethod
 from enum import Enum
 from typing import Any, Dict, List, Optional, Tuple
@@ -30,6 +29,7 @@ from synapse.storage.databases.main.search import SearchStore
 from synapse.types import JsonDict, ThirdPartyInstanceID
 from synapse.util import json_encoder
 from synapse.util.caches.descriptors import cached
+from synapse.util.stringutils import MXC_REGEX
 
 logger = logging.getLogger(__name__)
 
@@ -84,7 +84,7 @@ class RoomWorkerStore(SQLBaseStore):
         return await self.db_pool.simple_select_one(
             table="rooms",
             keyvalues={"room_id": room_id},
-            retcols=("room_id", "is_public", "creator"),
+            retcols=("room_id", "is_public", "creator", "has_auth_chain_index"),
             desc="get_room",
             allow_none=True,
         )
@@ -660,8 +660,6 @@ class RoomWorkerStore(SQLBaseStore):
             The local and remote media as a lists of tuples where the key is
             the hostname and the value is the media ID.
         """
-        mxc_re = re.compile("^mxc://([^/]+)/([^/#?]+)")
-
         sql = """
             SELECT stream_ordering, json FROM events
             JOIN event_json USING (room_id, event_id)
@@ -688,7 +686,7 @@ class RoomWorkerStore(SQLBaseStore):
                 for url in (content_url, thumbnail_url):
                     if not url:
                         continue
-                    matches = mxc_re.match(url)
+                    matches = MXC_REGEX.match(url)
                     if matches:
                         hostname = matches.group(1)
                         media_id = matches.group(2)
@@ -1166,6 +1164,37 @@ class RoomBackgroundUpdateStore(SQLBaseStore):
         # It's overridden by RoomStore for the synapse master.
         raise NotImplementedError()
 
+    async def has_auth_chain_index(self, room_id: str) -> bool:
+        """Check if the room has (or can have) a chain cover index.
+
+        Defaults to True if we don't have an entry in `rooms` table nor any
+        events for the room.
+        """
+
+        has_auth_chain_index = await self.db_pool.simple_select_one_onecol(
+            table="rooms",
+            keyvalues={"room_id": room_id},
+            retcol="has_auth_chain_index",
+            desc="has_auth_chain_index",
+            allow_none=True,
+        )
+
+        if has_auth_chain_index:
+            return True
+
+        # It's possible that we already have events for the room in our DB
+        # without a corresponding room entry. If we do then we don't want to
+        # mark the room as having an auth chain cover index.
+        max_ordering = await self.db_pool.simple_select_one_onecol(
+            table="events",
+            keyvalues={"room_id": room_id},
+            retcol="MAX(stream_ordering)",
+            allow_none=True,
+            desc="upsert_room_on_join",
+        )
+
+        return max_ordering is None
+
 
 class RoomStore(RoomBackgroundUpdateStore, RoomWorkerStore, SearchStore):
     def __init__(self, database: DatabasePool, db_conn, hs):
@@ -1179,12 +1208,21 @@ class RoomStore(RoomBackgroundUpdateStore, RoomWorkerStore, SearchStore):
         Called when we join a room over federation, and overwrites any room version
         currently in the table.
         """
+        # It's possible that we already have events for the room in our DB
+        # without a corresponding room entry. If we do then we don't want to
+        # mark the room as having an auth chain cover index.
+        has_auth_chain_index = await self.has_auth_chain_index(room_id)
+
         await self.db_pool.simple_upsert(
             desc="upsert_room_on_join",
             table="rooms",
             keyvalues={"room_id": room_id},
             values={"room_version": room_version.identifier},
-            insertion_values={"is_public": False, "creator": ""},
+            insertion_values={
+                "is_public": False,
+                "creator": "",
+                "has_auth_chain_index": has_auth_chain_index,
+            },
             # rooms has a unique constraint on room_id, so no need to lock when doing an
             # emulated upsert.
             lock=False,
@@ -1219,6 +1257,7 @@ class RoomStore(RoomBackgroundUpdateStore, RoomWorkerStore, SearchStore):
                         "creator": room_creator_user_id,
                         "is_public": is_public,
                         "room_version": room_version.identifier,
+                        "has_auth_chain_index": True,
                     },
                 )
                 if is_public:
@@ -1247,6 +1286,11 @@ class RoomStore(RoomBackgroundUpdateStore, RoomWorkerStore, SearchStore):
         When we receive an invite or any other event over federation that may relate to a room
         we are not in, store the version of the room if we don't already know the room version.
         """
+        # It's possible that we already have events for the room in our DB
+        # without a corresponding room entry. If we do then we don't want to
+        # mark the room as having an auth chain cover index.
+        has_auth_chain_index = await self.has_auth_chain_index(room_id)
+
         await self.db_pool.simple_upsert(
             desc="maybe_store_room_on_outlier_membership",
             table="rooms",
@@ -1256,6 +1300,7 @@ class RoomStore(RoomBackgroundUpdateStore, RoomWorkerStore, SearchStore):
                 "room_version": room_version.identifier,
                 "is_public": False,
                 "creator": "",
+                "has_auth_chain_index": has_auth_chain_index,
             },
             # rooms has a unique constraint on room_id, so no need to lock when doing an
             # emulated upsert.
diff --git a/synapse/storage/databases/main/roommember.py b/synapse/storage/databases/main/roommember.py
index dcdaf09682..92382bed28 100644
--- a/synapse/storage/databases/main/roommember.py
+++ b/synapse/storage/databases/main/roommember.py
@@ -873,8 +873,6 @@ class RoomMemberBackgroundUpdateStore(SQLBaseStore):
             "max_stream_id_exclusive", self._stream_order_on_start + 1
         )
 
-        INSERT_CLUMP_SIZE = 1000
-
         def add_membership_profile_txn(txn):
             sql = """
                 SELECT stream_ordering, event_id, events.room_id, event_json.json
@@ -915,9 +913,7 @@ class RoomMemberBackgroundUpdateStore(SQLBaseStore):
                 UPDATE room_memberships SET display_name = ?, avatar_url = ?
                 WHERE event_id = ? AND room_id = ?
             """
-            for index in range(0, len(to_update), INSERT_CLUMP_SIZE):
-                clump = to_update[index : index + INSERT_CLUMP_SIZE]
-                txn.executemany(to_update_sql, clump)
+            txn.execute_batch(to_update_sql, to_update)
 
             progress = {
                 "target_min_stream_id_inclusive": target_min_stream_id,
diff --git a/synapse/storage/databases/main/schema/delta/58/28drop_last_used_column.sql.postgres b/synapse/storage/databases/main/schema/delta/58/28drop_last_used_column.sql.postgres
new file mode 100644
index 0000000000..de57645019
--- /dev/null
+++ b/synapse/storage/databases/main/schema/delta/58/28drop_last_used_column.sql.postgres
@@ -0,0 +1,16 @@
+/* Copyright 2020 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.
+ */
+
+ALTER TABLE access_tokens DROP COLUMN last_used;
\ No newline at end of file
diff --git a/synapse/storage/databases/main/schema/delta/58/28drop_last_used_column.sql.sqlite b/synapse/storage/databases/main/schema/delta/58/28drop_last_used_column.sql.sqlite
new file mode 100644
index 0000000000..ee0e3521bf
--- /dev/null
+++ b/synapse/storage/databases/main/schema/delta/58/28drop_last_used_column.sql.sqlite
@@ -0,0 +1,62 @@
+/*
+ * Copyright 2020 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.
+ */
+
+ -- Dropping last_used column from access_tokens table.
+
+CREATE TABLE access_tokens2 (
+    id BIGINT PRIMARY KEY, 
+    user_id TEXT NOT NULL, 
+    device_id TEXT, 
+    token TEXT NOT NULL,
+    valid_until_ms BIGINT,
+    puppets_user_id TEXT,
+    last_validated BIGINT,
+    UNIQUE(token) 
+);
+
+INSERT INTO access_tokens2(id, user_id, device_id, token)
+    SELECT id, user_id, device_id, token FROM access_tokens;
+
+DROP TABLE access_tokens;
+ALTER TABLE access_tokens2 RENAME TO access_tokens;
+
+CREATE INDEX access_tokens_device_id ON access_tokens (user_id, device_id);
+
+
+-- Re-adding foreign key reference in event_txn_id table
+
+CREATE TABLE event_txn_id2 (
+    event_id TEXT NOT NULL,
+    room_id TEXT NOT NULL,
+    user_id TEXT NOT NULL,
+    token_id BIGINT NOT NULL,
+    txn_id TEXT NOT NULL,
+    inserted_ts BIGINT NOT NULL,
+    FOREIGN KEY (event_id)
+        REFERENCES events (event_id) ON DELETE CASCADE,
+    FOREIGN KEY (token_id)
+        REFERENCES access_tokens (id) ON DELETE CASCADE
+);
+
+INSERT INTO event_txn_id2(event_id, room_id, user_id, token_id, txn_id, inserted_ts)
+    SELECT event_id, room_id, user_id, token_id, txn_id, inserted_ts FROM event_txn_id;
+
+DROP TABLE event_txn_id;
+ALTER TABLE event_txn_id2 RENAME TO event_txn_id;
+
+CREATE UNIQUE INDEX IF NOT EXISTS event_txn_id_event_id ON event_txn_id(event_id);
+CREATE UNIQUE INDEX IF NOT EXISTS event_txn_id_txn_id ON event_txn_id(room_id, user_id, token_id, txn_id);
+CREATE INDEX IF NOT EXISTS event_txn_id_ts ON event_txn_id(inserted_ts);
\ No newline at end of file
diff --git a/synapse/storage/databases/main/schema/delta/58/28rejected_events_metadata.sql b/synapse/storage/databases/main/schema/delta/58/28rejected_events_metadata.sql
new file mode 100644
index 0000000000..9c95646281
--- /dev/null
+++ b/synapse/storage/databases/main/schema/delta/58/28rejected_events_metadata.sql
@@ -0,0 +1,17 @@
+/* Copyright 2020 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.
+ */
+
+INSERT INTO background_updates (ordering, update_name, progress_json) VALUES
+  (5828, 'rejected_events_metadata', '{}');
diff --git a/synapse/storage/databases/main/schema/delta/59/01ignored_user.py b/synapse/storage/databases/main/schema/delta/59/01ignored_user.py
index f35c70b699..9e8f35c1d2 100644
--- a/synapse/storage/databases/main/schema/delta/59/01ignored_user.py
+++ b/synapse/storage/databases/main/schema/delta/59/01ignored_user.py
@@ -55,7 +55,7 @@ def run_create(cur: Cursor, database_engine: BaseDatabaseEngine, *args, **kwargs
         # { "ignored_users": "@someone:example.org": {} }
         ignored_users = content.get("ignored_users", {})
         if isinstance(ignored_users, dict) and ignored_users:
-            cur.executemany(insert_sql, [(user_id, u) for u in ignored_users])
+            cur.execute_batch(insert_sql, [(user_id, u) for u in ignored_users])
 
     # Add indexes after inserting data for efficiency.
     logger.info("Adding constraints to ignored_users table")
diff --git a/synapse/storage/databases/main/schema/delta/59/04_event_auth_chains.sql b/synapse/storage/databases/main/schema/delta/59/04_event_auth_chains.sql
new file mode 100644
index 0000000000..729196cfd5
--- /dev/null
+++ b/synapse/storage/databases/main/schema/delta/59/04_event_auth_chains.sql
@@ -0,0 +1,52 @@
+/* Copyright 2020 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.
+ */
+
+-- See docs/auth_chain_difference_algorithm.md
+
+CREATE TABLE event_auth_chains (
+  event_id TEXT PRIMARY KEY,
+  chain_id BIGINT NOT NULL,
+  sequence_number BIGINT NOT NULL
+);
+
+CREATE UNIQUE INDEX event_auth_chains_c_seq_index ON event_auth_chains (chain_id, sequence_number);
+
+
+CREATE TABLE event_auth_chain_links (
+  origin_chain_id BIGINT NOT NULL,
+  origin_sequence_number BIGINT NOT NULL,
+
+  target_chain_id BIGINT NOT NULL,
+  target_sequence_number BIGINT NOT NULL
+);
+
+
+CREATE INDEX event_auth_chain_links_idx ON event_auth_chain_links (origin_chain_id, target_chain_id);
+
+
+-- Events that we have persisted but not calculated auth chains for,
+-- e.g. out of band memberships (where we don't have the auth chain)
+CREATE TABLE event_auth_chain_to_calculate (
+  event_id TEXT PRIMARY KEY,
+  room_id TEXT NOT NULL,
+  type TEXT NOT NULL,
+  state_key TEXT NOT NULL
+);
+
+CREATE INDEX event_auth_chain_to_calculate_rm_id ON event_auth_chain_to_calculate(room_id);
+
+
+-- Whether we've calculated the above index for a room.
+ALTER TABLE rooms ADD COLUMN has_auth_chain_index BOOLEAN;
diff --git a/synapse/storage/databases/main/schema/delta/59/04_event_auth_chains.sql.postgres b/synapse/storage/databases/main/schema/delta/59/04_event_auth_chains.sql.postgres
new file mode 100644
index 0000000000..e8a035bbeb
--- /dev/null
+++ b/synapse/storage/databases/main/schema/delta/59/04_event_auth_chains.sql.postgres
@@ -0,0 +1,16 @@
+/* Copyright 2020 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.
+ */
+
+CREATE SEQUENCE IF NOT EXISTS event_auth_chain_id;
diff --git a/synapse/storage/databases/main/schema/delta/59/04drop_account_data.sql b/synapse/storage/databases/main/schema/delta/59/04drop_account_data.sql
new file mode 100644
index 0000000000..64ab696cfe
--- /dev/null
+++ b/synapse/storage/databases/main/schema/delta/59/04drop_account_data.sql
@@ -0,0 +1,17 @@
+/* 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 is no longer used and was only kept until we bumped the schema version.
+DROP TABLE IF EXISTS account_data_max_stream_id;
diff --git a/synapse/storage/databases/main/schema/delta/59/05cache_invalidation.sql b/synapse/storage/databases/main/schema/delta/59/05cache_invalidation.sql
new file mode 100644
index 0000000000..fb71b360a0
--- /dev/null
+++ b/synapse/storage/databases/main/schema/delta/59/05cache_invalidation.sql
@@ -0,0 +1,17 @@
+/* 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 is no longer used and was only kept until we bumped the schema version.
+DROP TABLE IF EXISTS cache_invalidation_stream;
diff --git a/synapse/storage/databases/main/schema/delta/59/06chain_cover_index.sql b/synapse/storage/databases/main/schema/delta/59/06chain_cover_index.sql
new file mode 100644
index 0000000000..fe3dca71dd
--- /dev/null
+++ b/synapse/storage/databases/main/schema/delta/59/06chain_cover_index.sql
@@ -0,0 +1,17 @@
+/* Copyright 2020 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.
+ */
+
+INSERT INTO background_updates (ordering, update_name, progress_json, depends_on) VALUES
+  (5906, 'chain_cover', '{}', 'rejected_events_metadata');
diff --git a/synapse/storage/databases/main/schema/delta/59/06shard_account_data.sql b/synapse/storage/databases/main/schema/delta/59/06shard_account_data.sql
new file mode 100644
index 0000000000..46abf8d562
--- /dev/null
+++ b/synapse/storage/databases/main/schema/delta/59/06shard_account_data.sql
@@ -0,0 +1,20 @@
+/* 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.
+ */
+
+ALTER TABLE room_account_data ADD COLUMN instance_name TEXT;
+ALTER TABLE room_tags_revisions ADD COLUMN instance_name TEXT;
+ALTER TABLE account_data ADD COLUMN instance_name TEXT;
+
+ALTER TABLE receipts_linearized ADD COLUMN instance_name TEXT;
diff --git a/synapse/storage/databases/main/schema/delta/59/06shard_account_data.sql.postgres b/synapse/storage/databases/main/schema/delta/59/06shard_account_data.sql.postgres
new file mode 100644
index 0000000000..4a6e6c74f5
--- /dev/null
+++ b/synapse/storage/databases/main/schema/delta/59/06shard_account_data.sql.postgres
@@ -0,0 +1,32 @@
+/* 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.
+ */
+
+CREATE SEQUENCE IF NOT EXISTS account_data_sequence;
+
+-- We need to take the max across all the account_data tables as they share the
+-- ID generator
+SELECT setval('account_data_sequence', (
+    SELECT GREATEST(
+        (SELECT COALESCE(MAX(stream_id), 1) FROM room_account_data),
+        (SELECT COALESCE(MAX(stream_id), 1) FROM room_tags_revisions),
+        (SELECT COALESCE(MAX(stream_id), 1) FROM account_data)
+    )
+));
+
+CREATE SEQUENCE IF NOT EXISTS receipts_sequence;
+
+SELECT setval('receipts_sequence', (
+    SELECT COALESCE(MAX(stream_id), 1) FROM receipts_linearized
+));
diff --git a/synapse/storage/databases/main/schema/delta/59/07shard_account_data_fix.sql b/synapse/storage/databases/main/schema/delta/59/07shard_account_data_fix.sql
new file mode 100644
index 0000000000..9f2b5ebc5a
--- /dev/null
+++ b/synapse/storage/databases/main/schema/delta/59/07shard_account_data_fix.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.
+ */
+
+-- We incorrectly populated these, so we delete them and let the
+-- MultiWriterIdGenerator repopulate it.
+DELETE FROM stream_positions WHERE stream_name = 'receipts' OR stream_name = 'account_data';
diff --git a/synapse/storage/databases/main/search.py b/synapse/storage/databases/main/search.py
index e34fce6281..871af64b11 100644
--- a/synapse/storage/databases/main/search.py
+++ b/synapse/storage/databases/main/search.py
@@ -63,7 +63,7 @@ class SearchWorkerStore(SQLBaseStore):
                 for entry in entries
             )
 
-            txn.executemany(sql, args)
+            txn.execute_batch(sql, args)
 
         elif isinstance(self.database_engine, Sqlite3Engine):
             sql = (
@@ -75,7 +75,7 @@ class SearchWorkerStore(SQLBaseStore):
                 for entry in entries
             )
 
-            txn.executemany(sql, args)
+            txn.execute_batch(sql, args)
         else:
             # This should be unreachable.
             raise Exception("Unrecognized database engine")
diff --git a/synapse/storage/databases/main/tags.py b/synapse/storage/databases/main/tags.py
index 9f120d3cb6..50067eabfc 100644
--- a/synapse/storage/databases/main/tags.py
+++ b/synapse/storage/databases/main/tags.py
@@ -183,8 +183,6 @@ class TagsWorkerStore(AccountDataWorkerStore):
         )
         return {row["tag"]: db_to_json(row["content"]) for row in rows}
 
-
-class TagsStore(TagsWorkerStore):
     async def add_tag_to_room(
         self, user_id: str, room_id: str, tag: str, content: JsonDict
     ) -> int:
@@ -199,6 +197,8 @@ class TagsStore(TagsWorkerStore):
         Returns:
             The next account data ID.
         """
+        assert self._can_write_to_account_data
+
         content_json = json_encoder.encode(content)
 
         def add_tag_txn(txn, next_id):
@@ -223,6 +223,7 @@ class TagsStore(TagsWorkerStore):
         Returns:
             The next account data ID.
         """
+        assert self._can_write_to_account_data
 
         def remove_tag_txn(txn, next_id):
             sql = (
@@ -250,21 +251,12 @@ class TagsStore(TagsWorkerStore):
             room_id: The ID of the room.
             next_id: The the revision to advance to.
         """
+        assert self._can_write_to_account_data
 
         txn.call_after(
             self._account_data_stream_cache.entity_has_changed, user_id, next_id
         )
 
-        # Note: This is only here for backwards compat to allow admins to
-        # roll back to a previous Synapse version. Next time we update the
-        # database version we can remove this table.
-        update_max_id_sql = (
-            "UPDATE account_data_max_stream_id"
-            " SET stream_id = ?"
-            " WHERE stream_id < ?"
-        )
-        txn.execute(update_max_id_sql, (next_id, next_id))
-
         update_sql = (
             "UPDATE room_tags_revisions"
             " SET stream_id = ?"
@@ -288,3 +280,7 @@ class TagsStore(TagsWorkerStore):
                 # which stream_id ends up in the table, as long as it is higher
                 # than the id that the client has.
                 pass
+
+
+class TagsStore(TagsWorkerStore):
+    pass
diff --git a/synapse/storage/databases/main/transactions.py b/synapse/storage/databases/main/transactions.py
index 59207cadd4..cea595ff19 100644
--- a/synapse/storage/databases/main/transactions.py
+++ b/synapse/storage/databases/main/transactions.py
@@ -464,19 +464,17 @@ class TransactionStore(TransactionWorkerStore):
         txn: LoggingTransaction, now_time_ms: int, after_destination: Optional[str]
     ) -> List[str]:
         q = """
-            SELECT destination FROM destinations
-                WHERE destination IN (
-                    SELECT destination FROM destination_rooms
-                        WHERE destination_rooms.stream_ordering >
-                            destinations.last_successful_stream_ordering
-                )
-                AND destination > ?
-                AND (
-                    retry_last_ts IS NULL OR
-                    retry_last_ts + retry_interval < ?
-                )
-                ORDER BY destination
-                LIMIT 25
+            SELECT DISTINCT destination FROM destinations
+            INNER JOIN destination_rooms USING (destination)
+                WHERE
+                    stream_ordering > last_successful_stream_ordering
+                    AND destination > ?
+                    AND (
+                        retry_last_ts IS NULL OR
+                        retry_last_ts + retry_interval < ?
+                    )
+                    ORDER BY destination
+                    LIMIT 25
         """
         txn.execute(
             q,
diff --git a/synapse/storage/databases/state/store.py b/synapse/storage/databases/state/store.py
index 0e31cc811a..89cdc84a9c 100644
--- a/synapse/storage/databases/state/store.py
+++ b/synapse/storage/databases/state/store.py
@@ -565,11 +565,11 @@ class StateGroupDataStore(StateBackgroundUpdateStore, SQLBaseStore):
             )
 
         logger.info("[purge] removing redundant state groups")
-        txn.executemany(
+        txn.execute_batch(
             "DELETE FROM state_groups_state WHERE state_group = ?",
             ((sg,) for sg in state_groups_to_delete),
         )
-        txn.executemany(
+        txn.execute_batch(
             "DELETE FROM state_groups WHERE id = ?",
             ((sg,) for sg in state_groups_to_delete),
         )
diff --git a/synapse/storage/prepare_database.py b/synapse/storage/prepare_database.py
index 01efb2cabb..566ea19bae 100644
--- a/synapse/storage/prepare_database.py
+++ b/synapse/storage/prepare_database.py
@@ -35,9 +35,6 @@ logger = logging.getLogger(__name__)
 
 # Remember to update this number every time a change is made to database
 # schema files, so the users will be informed on server restarts.
-# XXX: If you're about to bump this to 59 (or higher) please create an update
-# that drops the unused `cache_invalidation_stream` table, as per #7436!
-# XXX: Also add an update to drop `account_data_max_stream_id` as per #7656!
 SCHEMA_VERSION = 59
 
 dir_path = os.path.abspath(os.path.dirname(__file__))
diff --git a/synapse/storage/util/id_generators.py b/synapse/storage/util/id_generators.py
index 133c0e7a28..71ef5a72dc 100644
--- a/synapse/storage/util/id_generators.py
+++ b/synapse/storage/util/id_generators.py
@@ -15,12 +15,11 @@
 import heapq
 import logging
 import threading
-from collections import deque
+from collections import OrderedDict
 from contextlib import contextmanager
-from typing import Dict, List, Optional, Set, Union
+from typing import Dict, List, Optional, Set, Tuple, Union
 
 import attr
-from typing_extensions import Deque
 
 from synapse.metrics.background_process_metrics import run_as_background_process
 from synapse.storage.database import DatabasePool, LoggingTransaction
@@ -101,7 +100,13 @@ class StreamIdGenerator:
             self._current = (max if step > 0 else min)(
                 self._current, _load_current_id(db_conn, table, column, step)
             )
-        self._unfinished_ids = deque()  # type: Deque[int]
+
+        # We use this as an ordered set, as we want to efficiently append items,
+        # remove items and get the first item. Since we insert IDs in order, the
+        # insertion ordering will ensure its in the correct ordering.
+        #
+        # The key and values are the same, but we never look at the values.
+        self._unfinished_ids = OrderedDict()  # type: OrderedDict[int, int]
 
     def get_next(self):
         """
@@ -113,7 +118,7 @@ class StreamIdGenerator:
             self._current += self._step
             next_id = self._current
 
-            self._unfinished_ids.append(next_id)
+            self._unfinished_ids[next_id] = next_id
 
         @contextmanager
         def manager():
@@ -121,7 +126,7 @@ class StreamIdGenerator:
                 yield next_id
             finally:
                 with self._lock:
-                    self._unfinished_ids.remove(next_id)
+                    self._unfinished_ids.pop(next_id)
 
         return _AsyncCtxManagerWrapper(manager())
 
@@ -140,7 +145,7 @@ class StreamIdGenerator:
             self._current += n * self._step
 
             for next_id in next_ids:
-                self._unfinished_ids.append(next_id)
+                self._unfinished_ids[next_id] = next_id
 
         @contextmanager
         def manager():
@@ -149,7 +154,7 @@ class StreamIdGenerator:
             finally:
                 with self._lock:
                     for next_id in next_ids:
-                        self._unfinished_ids.remove(next_id)
+                        self._unfinished_ids.pop(next_id)
 
         return _AsyncCtxManagerWrapper(manager())
 
@@ -162,7 +167,7 @@ class StreamIdGenerator:
         """
         with self._lock:
             if self._unfinished_ids:
-                return self._unfinished_ids[0] - self._step
+                return next(iter(self._unfinished_ids)) - self._step
 
             return self._current
 
@@ -186,11 +191,12 @@ class MultiWriterIdGenerator:
     Args:
         db_conn
         db
-        stream_name: A name for the stream.
+        stream_name: A name for the stream, for use in the `stream_positions`
+            table. (Does not need to be the same as the replication stream name)
         instance_name: The name of this instance.
-        table: Database table associated with stream.
-        instance_column: Column that stores the row's writer's instance name
-        id_column: Column that stores the stream ID.
+        tables: List of tables associated with the stream. Tuple of table
+            name, column name that stores the writer's instance name, and
+            column name that stores the stream ID.
         sequence_name: The name of the postgres sequence used to generate new
             IDs.
         writers: A list of known writers to use to populate current positions
@@ -206,9 +212,7 @@ class MultiWriterIdGenerator:
         db: DatabasePool,
         stream_name: str,
         instance_name: str,
-        table: str,
-        instance_column: str,
-        id_column: str,
+        tables: List[Tuple[str, str, str]],
         sequence_name: str,
         writers: List[str],
         positive: bool = True,
@@ -260,15 +264,20 @@ class MultiWriterIdGenerator:
         self._sequence_gen = PostgresSequenceGenerator(sequence_name)
 
         # We check that the table and sequence haven't diverged.
-        self._sequence_gen.check_consistency(
-            db_conn, table=table, id_column=id_column, positive=positive
-        )
+        for table, _, id_column in tables:
+            self._sequence_gen.check_consistency(
+                db_conn,
+                table=table,
+                id_column=id_column,
+                stream_name=stream_name,
+                positive=positive,
+            )
 
         # This goes and fills out the above state from the database.
-        self._load_current_ids(db_conn, table, instance_column, id_column)
+        self._load_current_ids(db_conn, tables)
 
     def _load_current_ids(
-        self, db_conn, table: str, instance_column: str, id_column: str
+        self, db_conn, tables: List[Tuple[str, str, str]],
     ):
         cur = db_conn.cursor(txn_name="_load_current_ids")
 
@@ -306,17 +315,22 @@ class MultiWriterIdGenerator:
             # We add a GREATEST here to ensure that the result is always
             # positive. (This can be a problem for e.g. backfill streams where
             # the server has never backfilled).
-            sql = """
-                SELECT GREATEST(COALESCE(%(agg)s(%(id)s), 1), 1)
-                FROM %(table)s
-            """ % {
-                "id": id_column,
-                "table": table,
-                "agg": "MAX" if self._positive else "-MIN",
-            }
-            cur.execute(sql)
-            (stream_id,) = cur.fetchone()
-            self._persisted_upto_position = stream_id
+            max_stream_id = 1
+            for table, _, id_column in tables:
+                sql = """
+                    SELECT GREATEST(COALESCE(%(agg)s(%(id)s), 1), 1)
+                    FROM %(table)s
+                """ % {
+                    "id": id_column,
+                    "table": table,
+                    "agg": "MAX" if self._positive else "-MIN",
+                }
+                cur.execute(sql)
+                (stream_id,) = cur.fetchone()
+
+                max_stream_id = max(max_stream_id, stream_id)
+
+            self._persisted_upto_position = max_stream_id
         else:
             # If we have a min_stream_id then we pull out everything greater
             # than it from the DB so that we can prefill
@@ -329,21 +343,28 @@ class MultiWriterIdGenerator:
             # stream positions table before restart (or the stream position
             # table otherwise got out of date).
 
-            sql = """
-                SELECT %(instance)s, %(id)s FROM %(table)s
-                WHERE ? %(cmp)s %(id)s
-            """ % {
-                "id": id_column,
-                "table": table,
-                "instance": instance_column,
-                "cmp": "<=" if self._positive else ">=",
-            }
-            cur.execute(sql, (min_stream_id * self._return_factor,))
-
             self._persisted_upto_position = min_stream_id
 
+            rows = []
+            for table, instance_column, id_column in tables:
+                sql = """
+                    SELECT %(instance)s, %(id)s FROM %(table)s
+                    WHERE ? %(cmp)s %(id)s
+                """ % {
+                    "id": id_column,
+                    "table": table,
+                    "instance": instance_column,
+                    "cmp": "<=" if self._positive else ">=",
+                }
+                cur.execute(sql, (min_stream_id * self._return_factor,))
+
+                rows.extend(cur)
+
+            # Sort so that we handle rows in order for each instance.
+            rows.sort()
+
             with self._lock:
-                for (instance, stream_id,) in cur:
+                for (instance, stream_id,) in rows:
                     stream_id = self._return_factor * stream_id
                     self._add_persisted_position(stream_id)
 
diff --git a/synapse/storage/util/sequence.py b/synapse/storage/util/sequence.py
index 4386b6101e..0ec4dc2918 100644
--- a/synapse/storage/util/sequence.py
+++ b/synapse/storage/util/sequence.py
@@ -15,9 +15,8 @@
 import abc
 import logging
 import threading
-from typing import Callable, List, Optional
+from typing import TYPE_CHECKING, Callable, List, Optional
 
-from synapse.storage.database import LoggingDatabaseConnection
 from synapse.storage.engines import (
     BaseDatabaseEngine,
     IncorrectDatabaseSetup,
@@ -25,6 +24,9 @@ from synapse.storage.engines import (
 )
 from synapse.storage.types import Connection, Cursor
 
+if TYPE_CHECKING:
+    from synapse.storage.database import LoggingDatabaseConnection
+
 logger = logging.getLogger(__name__)
 
 
@@ -43,6 +45,21 @@ and run the following SQL:
 See docs/postgres.md for more information.
 """
 
+_INCONSISTENT_STREAM_ERROR = """
+Postgres sequence '%(seq)s' is inconsistent with associated stream position
+of '%(stream_name)s' in the 'stream_positions' table.
+
+This is likely a programming error and should be reported at
+https://github.com/matrix-org/synapse.
+
+A temporary workaround to fix this error is to shut down Synapse (including
+any and all workers) and run the following SQL:
+
+    DELETE FROM stream_positions WHERE stream_name = '%(stream_name)s';
+
+This will need to be done every time the server is restarted.
+"""
+
 
 class SequenceGenerator(metaclass=abc.ABCMeta):
     """A class which generates a unique sequence of integers"""
@@ -53,19 +70,30 @@ class SequenceGenerator(metaclass=abc.ABCMeta):
         ...
 
     @abc.abstractmethod
+    def get_next_mult_txn(self, txn: Cursor, n: int) -> List[int]:
+        """Get the next `n` IDs in the sequence"""
+        ...
+
+    @abc.abstractmethod
     def check_consistency(
         self,
-        db_conn: LoggingDatabaseConnection,
+        db_conn: "LoggingDatabaseConnection",
         table: str,
         id_column: str,
+        stream_name: Optional[str] = None,
         positive: bool = True,
     ):
         """Should be called during start up to test that the current value of
         the sequence is greater than or equal to the maximum ID in the table.
 
-        This is to handle various cases where the sequence value can get out
-        of sync with the table, e.g. if Synapse gets rolled back to a previous
+        This is to handle various cases where the sequence value can get out of
+        sync with the table, e.g. if Synapse gets rolled back to a previous
         version and the rolled forwards again.
+
+        If a stream name is given then this will check that any value in the
+        `stream_positions` table is less than or equal to the current sequence
+        value. If it isn't then it's likely that streams have been crossed
+        somewhere (e.g. two ID generators have the same stream name).
         """
         ...
 
@@ -88,11 +116,15 @@ class PostgresSequenceGenerator(SequenceGenerator):
 
     def check_consistency(
         self,
-        db_conn: LoggingDatabaseConnection,
+        db_conn: "LoggingDatabaseConnection",
         table: str,
         id_column: str,
+        stream_name: Optional[str] = None,
         positive: bool = True,
     ):
+        """See SequenceGenerator.check_consistency for docstring.
+        """
+
         txn = db_conn.cursor(txn_name="sequence.check_consistency")
 
         # First we get the current max ID from the table.
@@ -116,6 +148,18 @@ class PostgresSequenceGenerator(SequenceGenerator):
             "SELECT last_value, is_called FROM %(seq)s" % {"seq": self._sequence_name}
         )
         last_value, is_called = txn.fetchone()
+
+        # If we have an associated stream check the stream_positions table.
+        max_in_stream_positions = None
+        if stream_name:
+            txn.execute(
+                "SELECT MAX(stream_id) FROM stream_positions WHERE stream_name = ?",
+                (stream_name,),
+            )
+            row = txn.fetchone()
+            if row:
+                max_in_stream_positions = row[0]
+
         txn.close()
 
         # If `is_called` is False then `last_value` is actually the value that
@@ -136,6 +180,14 @@ class PostgresSequenceGenerator(SequenceGenerator):
                 % {"seq": self._sequence_name, "table": table, "max_id_sql": table_sql}
             )
 
+        # If we have values in the stream positions table then they have to be
+        # less than or equal to `last_value`
+        if max_in_stream_positions and max_in_stream_positions > last_value:
+            raise IncorrectDatabaseSetup(
+                _INCONSISTENT_STREAM_ERROR
+                % {"seq": self._sequence_name, "stream_name": stream_name}
+            )
+
 
 GetFirstCallbackType = Callable[[Cursor], int]
 
@@ -172,8 +224,24 @@ class LocalSequenceGenerator(SequenceGenerator):
             self._current_max_id += 1
             return self._current_max_id
 
+    def get_next_mult_txn(self, txn: Cursor, n: int) -> List[int]:
+        with self._lock:
+            if self._current_max_id is None:
+                assert self._callback is not None
+                self._current_max_id = self._callback(txn)
+                self._callback = None
+
+            first_id = self._current_max_id + 1
+            self._current_max_id += n
+            return [first_id + i for i in range(n)]
+
     def check_consistency(
-        self, db_conn: Connection, table: str, id_column: str, positive: bool = True
+        self,
+        db_conn: Connection,
+        table: str,
+        id_column: str,
+        stream_name: Optional[str] = None,
+        positive: bool = True,
     ):
         # There is nothing to do for in memory sequences
         pass