| diff --git a/synapse/config/_base.py b/synapse/config/_base.py
index 2931a88207..a851f8801d 100644
--- a/synapse/config/_base.py
+++ b/synapse/config/_base.py
@@ -18,18 +18,18 @@
 import argparse
 import errno
 import os
-import time
-import urllib.parse
 from collections import OrderedDict
 from hashlib import sha256
 from textwrap import dedent
-from typing import Any, Callable, Iterable, List, MutableMapping, Optional
+from typing import Any, Iterable, List, MutableMapping, Optional
 
 import attr
 import jinja2
 import pkg_resources
 import yaml
 
+from synapse.util.templates import _create_mxc_to_http_filter, _format_ts_filter
+
 
 class ConfigError(Exception):
     """Represents a problem parsing the configuration
@@ -203,11 +203,28 @@ class Config:
         with open(file_path) as file_stream:
             return file_stream.read()
 
+    def read_template(self, filename: str) -> jinja2.Template:
+        """Load a template file from disk.
+
+        This function will attempt to load the given template from the default Synapse
+        template directory.
+
+        Files read are treated as Jinja templates. The templates is not rendered yet
+        and has autoescape enabled.
+
+        Args:
+            filename: A template filename to read.
+
+        Raises:
+            ConfigError: if the file's path is incorrect or otherwise cannot be read.
+
+        Returns:
+            A jinja2 template.
+        """
+        return self.read_templates([filename])[0]
+
     def read_templates(
-        self,
-        filenames: List[str],
-        custom_template_directory: Optional[str] = None,
-        autoescape: bool = False,
+        self, filenames: List[str], custom_template_directory: Optional[str] = None,
     ) -> List[jinja2.Template]:
         """Load a list of template files from disk using the given variables.
 
@@ -215,7 +232,8 @@ class Config:
         template directory. If `custom_template_directory` is supplied, that directory
         is tried first.
 
-        Files read are treated as Jinja templates. These templates are not rendered yet.
+        Files read are treated as Jinja templates. The templates are not rendered yet
+        and have autoescape enabled.
 
         Args:
             filenames: A list of template filenames to read.
@@ -223,16 +241,12 @@ class Config:
             custom_template_directory: A directory to try to look for the templates
                 before using the default Synapse template directory instead.
 
-            autoescape: Whether to autoescape variables before inserting them into the
-                template.
-
         Raises:
             ConfigError: if the file's path is incorrect or otherwise cannot be read.
 
         Returns:
             A list of jinja2 templates.
         """
-        templates = []
         search_directories = [self.default_template_dir]
 
         # The loader will first look in the custom template directory (if specified) for the
@@ -248,54 +262,20 @@ class Config:
             # Search the custom template directory as well
             search_directories.insert(0, custom_template_directory)
 
+        # TODO: switch to synapse.util.templates.build_jinja_env
         loader = jinja2.FileSystemLoader(search_directories)
-        env = jinja2.Environment(loader=loader, autoescape=autoescape)
+        env = jinja2.Environment(loader=loader, autoescape=jinja2.select_autoescape(),)
 
         # Update the environment with our custom filters
-        env.filters.update({"format_ts": _format_ts_filter})
-        if self.public_baseurl:
-            env.filters.update(
-                {"mxc_to_http": _create_mxc_to_http_filter(self.public_baseurl)}
-            )
-
-        for filename in filenames:
-            # Load the template
-            template = env.get_template(filename)
-            templates.append(template)
-
-        return templates
-
-
-def _format_ts_filter(value: int, format: str):
-    return time.strftime(format, time.localtime(value / 1000))
-
-
-def _create_mxc_to_http_filter(public_baseurl: str) -> Callable:
-    """Create and return a jinja2 filter that converts MXC urls to HTTP
-
-    Args:
-        public_baseurl: The public, accessible base URL of the homeserver
-    """
-
-    def mxc_to_http_filter(value, width, height, resize_method="crop"):
-        if value[0:6] != "mxc://":
-            return ""
-
-        server_and_media_id = value[6:]
-        fragment = None
-        if "#" in server_and_media_id:
-            server_and_media_id, fragment = server_and_media_id.split("#", 1)
-            fragment = "#" + fragment
-
-        params = {"width": width, "height": height, "method": resize_method}
-        return "%s_matrix/media/v1/thumbnail/%s?%s%s" % (
-            public_baseurl,
-            server_and_media_id,
-            urllib.parse.urlencode(params),
-            fragment or "",
+        env.filters.update(
+            {
+                "format_ts": _format_ts_filter,
+                "mxc_to_http": _create_mxc_to_http_filter(self.public_baseurl),
+            }
         )
 
-    return mxc_to_http_filter
+        # Load the templates
+        return [env.get_template(filename) for filename in filenames]
 
 
 class RootConfig:
diff --git a/synapse/config/_base.pyi b/synapse/config/_base.pyi
 index 29aa064e57..70025b5d60 100644
--- a/synapse/config/_base.pyi
+++ b/synapse/config/_base.pyi
@@ -9,6 +9,7 @@ from synapse.config import (
     consent_config,
     database,
     emailconfig,
+    experimental,
     groups,
     jwt_config,
     key,
@@ -18,6 +19,7 @@ from synapse.config import (
     password_auth_providers,
     push,
     ratelimiting,
+    redis,
     registration,
     repository,
     room_directory,
@@ -48,10 +50,11 @@ def path_exists(file_path: str): ...
 
 class RootConfig:
     server: server.ServerConfig
+    experimental: experimental.ExperimentalConfig
     tls: tls.TlsConfig
     database: database.DatabaseConfig
     logging: logger.LoggingConfig
-    ratelimit: ratelimiting.RatelimitConfig
+    ratelimiting: ratelimiting.RatelimitConfig
     media: repository.ContentRepositoryConfig
     captcha: captcha.CaptchaConfig
     voip: voip.VoipConfig
@@ -79,6 +82,7 @@ class RootConfig:
     roomdirectory: room_directory.RoomDirectoryConfig
     thirdpartyrules: third_party_event_rules.ThirdPartyRulesConfig
     tracer: tracer.TracerConfig
+    redis: redis.RedisConfig
 
     config_classes: List = ...
     def __init__(self) -> None: ...
diff --git a/synapse/config/captcha.py b/synapse/config/captcha.py
 index cb00958165..9e48f865cc 100644
--- a/synapse/config/captcha.py
+++ b/synapse/config/captcha.py
@@ -28,9 +28,7 @@ class CaptchaConfig(Config):
             "recaptcha_siteverify_api",
             "https://www.recaptcha.net/recaptcha/api/siteverify",
         )
-        self.recaptcha_template = self.read_templates(
-            ["recaptcha.html"], autoescape=True
-        )[0]
+        self.recaptcha_template = self.read_template("recaptcha.html")
 
     def generate_config_section(self, **kwargs):
         return """\
diff --git a/synapse/config/cas.py b/synapse/config/cas.py
 index c7877b4095..b226890c2a 100644
--- a/synapse/config/cas.py
+++ b/synapse/config/cas.py
@@ -30,7 +30,13 @@ class CasConfig(Config):
 
         if self.cas_enabled:
             self.cas_server_url = cas_config["server_url"]
-            self.cas_service_url = cas_config["service_url"]
+            public_base_url = cas_config.get("service_url") or self.public_baseurl
+            if public_base_url[-1] != "/":
+                public_base_url += "/"
+            # TODO Update this to a _synapse URL.
+            self.cas_service_url = (
+                public_base_url + "_matrix/client/r0/login/cas/ticket"
+            )
             self.cas_displayname_attribute = cas_config.get("displayname_attribute")
             self.cas_required_attributes = cas_config.get("required_attributes") or {}
         else:
@@ -53,10 +59,6 @@ class CasConfig(Config):
           #
           #server_url: "https://cas-server.com"
 
-          # The public URL of the homeserver.
-          #
-          #service_url: "https://homeserver.domain.com:8448"
-
           # The attribute of the CAS response to use as the display name.
           #
           # If unset, no displayname will be set.
diff --git a/synapse/config/consent_config.py b/synapse/config/consent_config.py
 index 6efa59b110..c47f364b14 100644
--- a/synapse/config/consent_config.py
+++ b/synapse/config/consent_config.py
@@ -89,7 +89,7 @@ class ConsentConfig(Config):
 
     def read_config(self, config, **kwargs):
         consent_config = config.get("user_consent")
-        self.terms_template = self.read_templates(["terms.html"], autoescape=True)[0]
+        self.terms_template = self.read_template("terms.html")
 
         if consent_config is None:
             return
diff --git a/synapse/config/emailconfig.py b/synapse/config/emailconfig.py
 index d4328c46b9..6a487afd34 100644
--- a/synapse/config/emailconfig.py
+++ b/synapse/config/emailconfig.py
@@ -166,11 +166,6 @@ class EmailConfig(Config):
             if not self.email_notif_from:
                 missing.append("email.notif_from")
 
-            # public_baseurl is required to build password reset and validation links that
-            # will be emailed to users
-            if config.get("public_baseurl") is None:
-                missing.append("public_baseurl")
-
             if missing:
                 raise ConfigError(
                     MISSING_PASSWORD_RESET_CONFIG_ERROR % (", ".join(missing),)
@@ -269,9 +264,6 @@ class EmailConfig(Config):
             if not self.email_notif_from:
                 missing.append("email.notif_from")
 
-            if config.get("public_baseurl") is None:
-                missing.append("public_baseurl")
-
             if missing:
                 raise ConfigError(
                     "email.enable_notifs is True but required keys are missing: %s"
diff --git a/synapse/config/experimental.py b/synapse/config/experimental.py
new file mode 100644
 index 0000000000..b1c1c51e4d
--- /dev/null
+++ b/synapse/config/experimental.py
@@ -0,0 +1,29 @@
+# -*- coding: utf-8 -*-
+# 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.
+
+from synapse.config._base import Config
+from synapse.types import JsonDict
+
+
+class ExperimentalConfig(Config):
+    """Config section for enabling experimental features"""
+
+    section = "experimental"
+
+    def read_config(self, config: JsonDict, **kwargs):
+        experimental = config.get("experimental_features") or {}
+
+        # MSC2858 (multiple SSO identity providers)
+        self.msc2858_enabled = experimental.get("msc2858_enabled", False)  # type: bool
diff --git a/synapse/config/homeserver.py b/synapse/config/homeserver.py
 index 4bd2b3587b..64a2429f77 100644
--- a/synapse/config/homeserver.py
+++ b/synapse/config/homeserver.py
@@ -24,6 +24,7 @@ from .cas import CasConfig
 from .consent_config import ConsentConfig
 from .database import DatabaseConfig
 from .emailconfig import EmailConfig
+from .experimental import ExperimentalConfig
 from .federation import FederationConfig
 from .groups import GroupsConfig
 from .jwt_config import JWTConfig
@@ -57,6 +58,7 @@ class HomeServerConfig(RootConfig):
 
     config_classes = [
         ServerConfig,
+        ExperimentalConfig,
         TlsConfig,
         FederationConfig,
         CacheConfig,
diff --git a/synapse/config/oidc_config.py b/synapse/config/oidc_config.py
 index 80a24cfbc9..4c24c50629 100644
--- a/synapse/config/oidc_config.py
+++ b/synapse/config/oidc_config.py
@@ -14,7 +14,7 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
-import string
+from collections import Counter
 from typing import Iterable, Optional, Tuple, Type
 
 import attr
@@ -23,6 +23,7 @@ from synapse.config._util import validate_config
 from synapse.python_dependencies import DependencyException, check_requirements
 from synapse.types import Collection, JsonDict
 from synapse.util.module_loader import load_module
+from synapse.util.stringutils import parse_and_validate_mxc_uri
 
 from ._base import Config, ConfigError
 
@@ -42,10 +43,17 @@ class OIDCConfig(Config):
         except DependencyException as e:
             raise ConfigError(e.message) from e
 
-        public_baseurl = self.public_baseurl
-        if public_baseurl is None:
-            raise ConfigError("oidc_config requires a public_baseurl to be set")
-        self.oidc_callback_url = public_baseurl + "_synapse/oidc/callback"
+        # check we don't have any duplicate idp_ids now. (The SSO handler will also
+        # check for duplicates when the REST listeners get registered, but that happens
+        # after synapse has forked so doesn't give nice errors.)
+        c = Counter([i.idp_id for i in self.oidc_providers])
+        for idp_id, count in c.items():
+            if count > 1:
+                raise ConfigError(
+                    "Multiple OIDC providers have the idp_id %r." % idp_id
+                )
+
+        self.oidc_callback_url = self.public_baseurl + "_synapse/client/oidc/callback"
 
     @property
     def oidc_enabled(self) -> bool:
@@ -68,6 +76,16 @@ class OIDCConfig(Config):
         #   idp_name: A user-facing name for this identity provider, which is used to
         #       offer the user a choice of login mechanisms.
         #
+        #   idp_icon: An optional icon for this identity provider, which is presented
+        #       by clients and Synapse's own IdP picker page. If given, must be an
+        #       MXC URI of the format mxc://<server-name>/<media-id>. (An easy way to
+        #       obtain such an MXC URI is to upload an image to an (unencrypted) room
+        #       and then copy the "url" from the source of the event.)
+        #
+        #   idp_brand: An optional brand for this identity provider, allowing clients
+        #       to style the login flow according to the identity provider in question.
+        #       See the spec for possible options here.
+        #
         #   discover: set to 'false' to disable the use of the OIDC discovery mechanism
         #       to discover endpoints. Defaults to true.
         #
@@ -127,17 +145,21 @@ class OIDCConfig(Config):
         #
         #           For the default provider, the following settings are available:
         #
-        #             sub: name of the claim containing a unique identifier for the
-        #                 user. Defaults to 'sub', which OpenID Connect compliant
-        #                 providers should provide.
+        #             subject_claim: name of the claim containing a unique identifier
+        #                 for the user. Defaults to 'sub', which OpenID Connect
+        #                 compliant providers should provide.
         #
         #             localpart_template: Jinja2 template for the localpart of the MXID.
         #                 If this is not set, the user will be prompted to choose their
-        #                 own username.
+        #                 own username (see 'sso_auth_account_details.html' in the 'sso'
+        #                 section of this file).
         #
         #             display_name_template: Jinja2 template for the display name to set
         #                 on first login. If unset, no displayname will be set.
         #
+        #             email_template: Jinja2 template for the email address of the user.
+        #                 If unset, no email address will be added to the account.
+        #
         #             extra_attributes: a map of Jinja2 templates for extra attributes
         #                 to send back to the client during login.
         #                 Note that these are non-standard and clients will ignore them
@@ -152,13 +174,16 @@ class OIDCConfig(Config):
         #
         # For backwards compatibility, it is also possible to configure a single OIDC
         # provider via an 'oidc_config' setting. This is now deprecated and admins are
-        # advised to migrate to the 'oidc_providers' format.
+        # advised to migrate to the 'oidc_providers' format. (When doing that migration,
+        # use 'oidc' for the idp_id to ensure that existing users continue to be
+        # recognised.)
         #
         oidc_providers:
           # Generic example
           #
           #- idp_id: my_idp
           #  idp_name: "My OpenID provider"
+          #  idp_icon: "mxc://example.com/mediaid"
           #  discover: false
           #  issuer: "https://accounts.example.com/"
           #  client_id: "provided-by-your-issuer"
@@ -170,6 +195,12 @@ class OIDCConfig(Config):
           #  userinfo_endpoint: "https://accounts.example.com/userinfo"
           #  jwks_uri: "https://accounts.example.com/.well-known/jwks.json"
           #  skip_verification: true
+          #  user_mapping_provider:
+          #    config:
+          #      subject_claim: "id"
+          #      localpart_template: "{{ user.login }}"
+          #      display_name_template: "{{ user.name }}"
+          #      email_template: "{{ user.email }}"
 
           # For use with Keycloak
           #
@@ -182,8 +213,9 @@ class OIDCConfig(Config):
 
           # For use with Github
           #
-          #- idp_id: google
-          #  idp_name: Google
+          #- idp_id: github
+          #  idp_name: Github
+          #  idp_brand: org.matrix.github
           #  discover: false
           #  issuer: "https://github.com/"
           #  client_id: "your-client-id" # TO BE FILLED
@@ -207,8 +239,22 @@ OIDC_PROVIDER_CONFIG_SCHEMA = {
     "type": "object",
     "required": ["issuer", "client_id", "client_secret"],
     "properties": {
-        "idp_id": {"type": "string", "minLength": 1, "maxLength": 128},
+        "idp_id": {
+            "type": "string",
+            "minLength": 1,
+            # MSC2858 allows a maxlen of 255, but we prefix with "oidc-"
+            "maxLength": 250,
+            "pattern": "^[A-Za-z0-9._~-]+$",
+        },
         "idp_name": {"type": "string"},
+        "idp_icon": {"type": "string"},
+        "idp_brand": {
+            "type": "string",
+            # MSC2758-style namespaced identifier
+            "minLength": 1,
+            "maxLength": 255,
+            "pattern": "^[a-z][a-z0-9_.-]*$",
+        },
         "discover": {"type": "boolean"},
         "issuer": {"type": "string"},
         "client_id": {"type": "string"},
@@ -327,20 +373,34 @@ def _parse_oidc_config_dict(
             config_path + ("user_mapping_provider", "module"),
         )
 
-    # MSC2858 will appy certain limits in what can be used as an IdP id, so let's
-    # enforce those limits now.
     idp_id = oidc_config.get("idp_id", "oidc")
-    valid_idp_chars = set(string.ascii_letters + string.digits + "-._~")
 
-    if any(c not in valid_idp_chars for c in idp_id):
-        raise ConfigError(
-            'idp_id may only contain A-Z, a-z, 0-9, "-", ".", "_", "~"',
-            config_path + ("idp_id",),
-        )
+    # prefix the given IDP with a prefix specific to the SSO mechanism, to avoid
+    # clashes with other mechs (such as SAML, CAS).
+    #
+    # We allow "oidc" as an exception so that people migrating from old-style
+    # "oidc_config" format (which has long used "oidc" as its idp_id) can migrate to
+    # a new-style "oidc_providers" entry without changing the idp_id for their provider
+    # (and thereby invalidating their user_external_ids data).
+
+    if idp_id != "oidc":
+        idp_id = "oidc-" + idp_id
+
+    # MSC2858 also specifies that the idp_icon must be a valid MXC uri
+    idp_icon = oidc_config.get("idp_icon")
+    if idp_icon is not None:
+        try:
+            parse_and_validate_mxc_uri(idp_icon)
+        except ValueError as e:
+            raise ConfigError(
+                "idp_icon must be a valid MXC URI", config_path + ("idp_icon",)
+            ) from e
 
     return OidcProviderConfig(
         idp_id=idp_id,
         idp_name=oidc_config.get("idp_name", "OIDC"),
+        idp_icon=idp_icon,
+        idp_brand=oidc_config.get("idp_brand"),
         discover=oidc_config.get("discover", True),
         issuer=oidc_config["issuer"],
         client_id=oidc_config["client_id"],
@@ -368,6 +428,12 @@ class OidcProviderConfig:
     # user-facing name for this identity provider.
     idp_name = attr.ib(type=str)
 
+    # Optional MXC URI for icon for this IdP.
+    idp_icon = attr.ib(type=Optional[str])
+
+    # Optional brand identifier for this IdP.
+    idp_brand = attr.ib(type=Optional[str])
+
     # whether the OIDC discovery mechanism is used to discover endpoints
     discover = attr.ib(type=bool)
 
diff --git a/synapse/config/ratelimiting.py b/synapse/config/ratelimiting.py
 index 14b8836197..def33a60ad 100644
--- a/synapse/config/ratelimiting.py
+++ b/synapse/config/ratelimiting.py
@@ -24,7 +24,7 @@ class RateLimitConfig:
         defaults={"per_second": 0.17, "burst_count": 3.0},
     ):
         self.per_second = config.get("per_second", defaults["per_second"])
-        self.burst_count = config.get("burst_count", defaults["burst_count"])
+        self.burst_count = int(config.get("burst_count", defaults["burst_count"]))
 
 
 class FederationRateLimitConfig:
@@ -102,6 +102,20 @@ class RatelimitConfig(Config):
             defaults={"per_second": 0.01, "burst_count": 3},
         )
 
+        self.rc_3pid_validation = RateLimitConfig(
+            config.get("rc_3pid_validation") or {},
+            defaults={"per_second": 0.003, "burst_count": 5},
+        )
+
+        self.rc_invites_per_room = RateLimitConfig(
+            config.get("rc_invites", {}).get("per_room", {}),
+            defaults={"per_second": 0.3, "burst_count": 10},
+        )
+        self.rc_invites_per_user = RateLimitConfig(
+            config.get("rc_invites", {}).get("per_user", {}),
+            defaults={"per_second": 0.003, "burst_count": 5},
+        )
+
     def generate_config_section(self, **kwargs):
         return """\
         ## Ratelimiting ##
@@ -131,6 +145,9 @@ class RatelimitConfig(Config):
         #     users are joining rooms the server is already in (this is cheap) vs
         #     "remote" for when users are trying to join rooms not on the server (which
         #     can be more expensive)
+        #   - one for ratelimiting how often a user or IP can attempt to validate a 3PID.
+        #   - two for ratelimiting how often invites can be sent in a room or to a
+        #     specific user.
         #
         # The defaults are as shown below.
         #
@@ -164,7 +181,18 @@ class RatelimitConfig(Config):
         #  remote:
         #    per_second: 0.01
         #    burst_count: 3
-
+        #
+        #rc_3pid_validation:
+        #  per_second: 0.003
+        #  burst_count: 5
+        #
+        #rc_invites:
+        #  per_room:
+        #    per_second: 0.3
+        #    burst_count: 10
+        #  per_user:
+        #    per_second: 0.003
+        #    burst_count: 5
 
         # Ratelimiting settings for incoming federation
         #
diff --git a/synapse/config/registration.py b/synapse/config/registration.py
 index 740c3fc1b1..ac48913a0b 100644
--- a/synapse/config/registration.py
+++ b/synapse/config/registration.py
@@ -49,10 +49,6 @@ class AccountValidityConfig(Config):
 
             self.startup_job_max_delta = self.period * 10.0 / 100.0
 
-        if self.renew_by_email_enabled:
-            if "public_baseurl" not in synapse_config:
-                raise ConfigError("Can't send renewal emails without 'public_baseurl'")
-
         template_dir = config.get("template_dir")
 
         if not template_dir:
@@ -109,13 +105,6 @@ class RegistrationConfig(Config):
         account_threepid_delegates = config.get("account_threepid_delegates") or {}
         self.account_threepid_delegate_email = account_threepid_delegates.get("email")
         self.account_threepid_delegate_msisdn = account_threepid_delegates.get("msisdn")
-        if self.account_threepid_delegate_msisdn and not self.public_baseurl:
-            raise ConfigError(
-                "The configuration option `public_baseurl` is required if "
-                "`account_threepid_delegate.msisdn` is set, such that "
-                "clients know where to submit validation tokens to. Please "
-                "configure `public_baseurl`."
-            )
 
         self.default_identity_server = config.get("default_identity_server")
         self.allow_guest_access = config.get("allow_guest_access", False)
@@ -187,9 +176,7 @@ class RegistrationConfig(Config):
         self.session_lifetime = session_lifetime
 
         # The success template used during fallback auth.
-        self.fallback_success_template = self.read_templates(
-            ["auth_success.html"], autoescape=True
-        )[0]
+        self.fallback_success_template = self.read_template("auth_success.html")
 
     def generate_config_section(self, generate_secrets=False, **kwargs):
         if generate_secrets:
@@ -240,8 +227,9 @@ class RegistrationConfig(Config):
           # send an email to the account's email address with a renewal link. By
           # default, no such emails are sent.
           #
-          # If you enable this setting, you will also need to fill out the 'email' and
-          # 'public_baseurl' configuration sections.
+          # If you enable this setting, you will also need to fill out the 'email'
+          # configuration section. You should also check that 'public_baseurl' is set
+          # correctly.
           #
           #renew_at: 1w
 
@@ -332,8 +320,7 @@ class RegistrationConfig(Config):
         # The identity server which we suggest that clients should use when users log
         # in on this server.
         #
-        # (By default, no suggestion is made, so it is left up to the client.
-        # This setting is ignored unless public_baseurl is also set.)
+        # (By default, no suggestion is made, so it is left up to the client.)
         #
         #default_identity_server: https://matrix.org
 
@@ -358,8 +345,6 @@ class RegistrationConfig(Config):
         # by the Matrix Identity Service API specification:
         # https://matrix.org/docs/spec/identity_service/latest
         #
-        # If a delegate is specified, the config option public_baseurl must also be filled out.
-        #
         account_threepid_delegates:
             #email: https://example.com     # Delegate email sending to example.com
             #msisdn: http://localhost:8090  # Delegate SMS sending to this local process
diff --git a/synapse/config/saml2_config.py b/synapse/config/saml2_config.py
 index 7b97d4f114..ad865a667f 100644
--- a/synapse/config/saml2_config.py
+++ b/synapse/config/saml2_config.py
@@ -189,15 +189,13 @@ class SAML2Config(Config):
         import saml2
 
         public_baseurl = self.public_baseurl
-        if public_baseurl is None:
-            raise ConfigError("saml2_config requires a public_baseurl to be set")
 
         if self.saml2_grandfathered_mxid_source_attribute:
             optional_attributes.add(self.saml2_grandfathered_mxid_source_attribute)
         optional_attributes -= required_attributes
 
-        metadata_url = public_baseurl + "_matrix/saml2/metadata.xml"
-        response_url = public_baseurl + "_matrix/saml2/authn_response"
+        metadata_url = public_baseurl + "_synapse/client/saml2/metadata.xml"
+        response_url = public_baseurl + "_synapse/client/saml2/authn_response"
         return {
             "entityid": metadata_url,
             "service": {
@@ -235,10 +233,10 @@ class SAML2Config(Config):
         # enable SAML login.
         #
         # Once SAML support is enabled, a metadata file will be exposed at
-        # https://<server>:<port>/_matrix/saml2/metadata.xml, which you may be able to
+        # https://<server>:<port>/_synapse/client/saml2/metadata.xml, which you may be able to
         # use to configure your SAML IdP with. Alternatively, you can manually configure
         # the IdP to use an ACS location of
-        # https://<server>:<port>/_matrix/saml2/authn_response.
+        # https://<server>:<port>/_synapse/client/saml2/authn_response.
         #
         saml2_config:
           # `sp_config` is the configuration for the pysaml2 Service Provider.
diff --git a/synapse/config/server.py b/synapse/config/server.py
 index 7242a4aa8e..47a0370173 100644
--- a/synapse/config/server.py
+++ b/synapse/config/server.py
@@ -26,7 +26,7 @@ import yaml
 from netaddr import IPSet
 
 from synapse.api.room_versions import KNOWN_ROOM_VERSIONS
-from synapse.http.endpoint import parse_and_validate_server_name
+from synapse.util.stringutils import parse_and_validate_server_name
 
 from ._base import Config, ConfigError
 
@@ -161,7 +161,11 @@ class ServerConfig(Config):
         self.print_pidfile = config.get("print_pidfile")
         self.user_agent_suffix = config.get("user_agent_suffix")
         self.use_frozen_dicts = config.get("use_frozen_dicts", False)
-        self.public_baseurl = config.get("public_baseurl")
+        self.public_baseurl = config.get("public_baseurl") or "https://%s/" % (
+            self.server_name,
+        )
+        if self.public_baseurl[-1] != "/":
+            self.public_baseurl += "/"
 
         # Whether to enable user presence.
         self.use_presence = config.get("use_presence", True)
@@ -317,9 +321,6 @@ class ServerConfig(Config):
         # Always blacklist 0.0.0.0, ::
         self.federation_ip_range_blacklist.update(["0.0.0.0", "::"])
 
-        if self.public_baseurl is not None:
-            if self.public_baseurl[-1] != "/":
-                self.public_baseurl += "/"
         self.start_pushers = config.get("start_pushers", True)
 
         # (undocumented) option for torturing the worker-mode replication a bit,
@@ -740,11 +741,16 @@ class ServerConfig(Config):
         #
         #web_client_location: https://riot.example.com/
 
-        # The public-facing base URL that clients use to access this HS
-        # (not including _matrix/...). This is the same URL a user would
-        # enter into the 'custom HS URL' field on their client. If you
-        # use synapse with a reverse proxy, this should be the URL to reach
-        # synapse via the proxy.
+        # The public-facing base URL that clients use to access this Homeserver (not
+        # including _matrix/...). This is the same URL a user might enter into the
+        # 'Custom Homeserver URL' field on their client. If you use Synapse with a
+        # reverse proxy, this should be the URL to reach Synapse via the proxy.
+        # Otherwise, it should be the URL to reach Synapse's client HTTP listener (see
+        # 'listeners' below).
+        #
+        # If this is left unset, it defaults to 'https://<server_name>/'. (Note that
+        # that will not work unless you configure Synapse or a reverse-proxy to listen
+        # on port 443.)
         #
         #public_baseurl: https://example.com/
 
diff --git a/synapse/config/sso.py b/synapse/config/sso.py
 index 366f0d4698..939eeac6de 100644
--- a/synapse/config/sso.py
+++ b/synapse/config/sso.py
@@ -27,7 +27,7 @@ class SSOConfig(Config):
         sso_config = config.get("sso") or {}  # type: Dict[str, Any]
 
         # The sso-specific template_dir
-        template_dir = sso_config.get("template_dir")
+        self.sso_template_dir = sso_config.get("template_dir")
 
         # Read templates from disk
         (
@@ -48,7 +48,7 @@ class SSOConfig(Config):
                 "sso_auth_success.html",
                 "sso_auth_bad_user.html",
             ],
-            template_dir,
+            self.sso_template_dir,
         )
 
         # These templates have no placeholders, so render them here
@@ -64,11 +64,8 @@ class SSOConfig(Config):
         # gracefully to the client). This would make it pointless to ask the user for
         # confirmation, since the URL the confirmation page would be showing wouldn't be
         # the client's.
-        # public_baseurl is an optional setting, so we only add the fallback's URL to the
-        # list if it's provided (because we can't figure out what that URL is otherwise).
-        if self.public_baseurl:
-            login_fallback_url = self.public_baseurl + "_matrix/static/client/login"
-            self.sso_client_whitelist.append(login_fallback_url)
+        login_fallback_url = self.public_baseurl + "_matrix/static/client/login"
+        self.sso_client_whitelist.append(login_fallback_url)
 
     def generate_config_section(self, **kwargs):
         return """\
@@ -86,9 +83,9 @@ class SSOConfig(Config):
             # phishing attacks from evil.site. To avoid this, include a slash after the
             # hostname: "https://my.client/".
             #
-            # If public_baseurl is set, then the login fallback page (used by clients
-            # that don't natively support the required login flows) is whitelisted in
-            # addition to any URLs in this list.
+            # The login fallback page (used by clients that don't natively support the
+            # required login flows) is automatically whitelisted in addition to any URLs
+            # in this list.
             #
             # By default, this list is empty.
             #
@@ -116,8 +113,13 @@ class SSOConfig(Config):
             #
             #     * providers: a list of available Identity Providers. Each element is
             #       an object with the following attributes:
+            #
             #         * idp_id: unique identifier for the IdP
             #         * idp_name: user-facing name for the IdP
+            #         * idp_icon: if specified in the IdP config, an MXC URI for an icon
+            #              for the IdP
+            #         * idp_brand: if specified in the IdP config, a textual identifier
+            #              for the brand of the IdP
             #
             #   The rendered HTML page should contain a form which submits its results
             #   back as a GET request, with the following query parameters:
@@ -127,10 +129,62 @@ class SSOConfig(Config):
             #
             #     * idp: the 'idp_id' of the chosen IDP.
             #
+            # * HTML page to prompt new users to enter a userid and confirm other
+            #   details: 'sso_auth_account_details.html'. This is only shown if the
+            #   SSO implementation (with any user_mapping_provider) does not return
+            #   a localpart.
+            #
+            #   When rendering, this template is given the following variables:
+            #
+            #     * server_name: the homeserver's name.
+            #
+            #     * idp: details of the SSO Identity Provider that the user logged in
+            #       with: an object with the following attributes:
+            #
+            #         * idp_id: unique identifier for the IdP
+            #         * idp_name: user-facing name for the IdP
+            #         * idp_icon: if specified in the IdP config, an MXC URI for an icon
+            #              for the IdP
+            #         * idp_brand: if specified in the IdP config, a textual identifier
+            #              for the brand of the IdP
+            #
+            #     * user_attributes: an object containing details about the user that
+            #       we received from the IdP. May have the following attributes:
+            #
+            #         * display_name: the user's display_name
+            #         * emails: a list of email addresses
+            #
+            #   The template should render a form which submits the following fields:
+            #
+            #     * username: the localpart of the user's chosen user id
+            #
+            # * HTML page allowing the user to consent to the server's terms and
+            #   conditions. This is only shown for new users, and only if
+            #   `user_consent.require_at_registration` is set.
+            #
+            #   When rendering, this template is given the following variables:
+            #
+            #     * server_name: the homeserver's name.
+            #
+            #     * user_id: the user's matrix proposed ID.
+            #
+            #     * user_profile.display_name: the user's proposed display name, if any.
+            #
+            #     * consent_version: the version of the terms that the user will be
+            #       shown
+            #
+            #     * terms_url: a link to the page showing the terms.
+            #
+            #   The template should render a form which submits the following fields:
+            #
+            #     * accepted_version: the version of the terms accepted by the user
+            #       (ie, 'consent_version' from the input variables).
+            #
             # * HTML page for a confirmation step before redirecting back to the client
             #   with the login token: 'sso_redirect_confirm.html'.
             #
-            #   When rendering, this template is given three variables:
+            #   When rendering, this template is given the following variables:
+            #
             #     * redirect_url: the URL the user is about to be redirected to. Needs
             #                     manual escaping (see
             #                     https://jinja.palletsprojects.com/en/2.11.x/templates/#html-escaping).
@@ -143,6 +197,17 @@ class SSOConfig(Config):
             #
             #     * server_name: the homeserver's name.
             #
+            #     * new_user: a boolean indicating whether this is the user's first time
+            #          logging in.
+            #
+            #     * user_id: the user's matrix ID.
+            #
+            #     * user_profile.avatar_url: an MXC URI for the user's avatar, if any.
+            #           None if the user has not set an avatar.
+            #
+            #     * user_profile.display_name: the user's display name. None if the user
+            #           has not set a display name.
+            #
             # * HTML page which notifies the user that they are authenticating to confirm
             #   an operation on their account during the user interactive authentication
             #   process: 'sso_auth_confirm.html'.
@@ -154,6 +219,16 @@ class SSOConfig(Config):
             #
             #     * description: the operation which the user is being asked to confirm
             #
+            #     * idp: details of the Identity Provider that we will use to confirm
+            #       the user's identity: an object with the following attributes:
+            #
+            #         * idp_id: unique identifier for the IdP
+            #         * idp_name: user-facing name for the IdP
+            #         * idp_icon: if specified in the IdP config, an MXC URI for an icon
+            #              for the IdP
+            #         * idp_brand: if specified in the IdP config, a textual identifier
+            #              for the brand of the IdP
+            #
             # * HTML page shown after a successful user interactive authentication session:
             #   'sso_auth_success.html'.
             #
 |