| diff --git a/synapse/rest/admin/__init__.py b/synapse/rest/admin/__init__.py
index b7121c0c26..065e7c3e68 100644
--- a/synapse/rest/admin/__init__.py
+++ b/synapse/rest/admin/__init__.py
@@ -1,6 +1,8 @@
 # -*- coding: utf-8 -*-
 # Copyright 2014-2016 OpenMarket Ltd
 # Copyright 2018-2019 New Vector 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.
@@ -40,11 +42,13 @@ from synapse.rest.admin.media import ListMediaInRoom, register_servlets_for_medi
 from synapse.rest.admin.purge_room_servlet import PurgeRoomServlet
 from synapse.rest.admin.rooms import (
     DeleteRoomRestServlet,
+    ForwardExtremitiesRestServlet,
     JoinRoomAliasServlet,
     ListRoomRestServlet,
     MakeRoomAdminRestServlet,
     RoomMembersRestServlet,
     RoomRestServlet,
+    RoomStateRestServlet,
     ShutdownRoomRestServlet,
 )
 from synapse.rest.admin.server_notice_servlet import SendServerNoticeServlet
@@ -55,6 +59,7 @@ from synapse.rest.admin.users import (
     PushersRestServlet,
     ResetPasswordRestServlet,
     SearchUsersRestServlet,
+    ShadowBanRestServlet,
     UserAdminServlet,
     UserMediaRestServlet,
     UserMembershipRestServlet,
@@ -213,6 +218,7 @@ def register_servlets(hs, http_server):
     """
     register_servlets_for_client_rest_resource(hs, http_server)
     ListRoomRestServlet(hs).register(http_server)
+    RoomStateRestServlet(hs).register(http_server)
     RoomRestServlet(hs).register(http_server)
     RoomMembersRestServlet(hs).register(http_server)
     DeleteRoomRestServlet(hs).register(http_server)
@@ -234,6 +240,8 @@ def register_servlets(hs, http_server):
     EventReportsRestServlet(hs).register(http_server)
     PushersRestServlet(hs).register(http_server)
     MakeRoomAdminRestServlet(hs).register(http_server)
+    ShadowBanRestServlet(hs).register(http_server)
+    ForwardExtremitiesRestServlet(hs).register(http_server)
 
 
 def register_servlets_for_client_rest_resource(hs, http_server):
diff --git a/synapse/rest/admin/rooms.py b/synapse/rest/admin/rooms.py
 index ab7cc9102a..3e57e6a4d0 100644
--- a/synapse/rest/admin/rooms.py
+++ b/synapse/rest/admin/rooms.py
@@ -1,5 +1,5 @@
 # -*- coding: utf-8 -*-
-# Copyright 2019 The Matrix.org Foundation C.I.C.
+# Copyright 2019-2021 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.
@@ -292,6 +292,45 @@ class RoomMembersRestServlet(RestServlet):
         return 200, ret
 
 
+class RoomStateRestServlet(RestServlet):
+    """
+    Get full state within a room.
+    """
+
+    PATTERNS = admin_patterns("/rooms/(?P<room_id>[^/]+)/state")
+
+    def __init__(self, hs: "HomeServer"):
+        self.hs = hs
+        self.auth = hs.get_auth()
+        self.store = hs.get_datastore()
+        self.clock = hs.get_clock()
+        self._event_serializer = hs.get_event_client_serializer()
+
+    async def on_GET(
+        self, request: SynapseRequest, room_id: str
+    ) -> Tuple[int, JsonDict]:
+        requester = await self.auth.get_user_by_req(request)
+        await assert_user_is_admin(self.auth, requester.user)
+
+        ret = await self.store.get_room(room_id)
+        if not ret:
+            raise NotFoundError("Room not found")
+
+        event_ids = await self.store.get_current_state_ids(room_id)
+        events = await self.store.get_events(event_ids.values())
+        now = self.clock.time_msec()
+        room_state = await self._event_serializer.serialize_events(
+            events.values(),
+            now,
+            # We don't bother bundling aggregations in when asked for state
+            # events, as clients won't use them.
+            bundle_aggregations=False,
+        )
+        ret = {"state": room_state}
+
+        return 200, ret
+
+
 class JoinRoomAliasServlet(RestServlet):
 
     PATTERNS = admin_patterns("/join/(?P<room_identifier>[^/]*)")
@@ -431,7 +470,17 @@ class MakeRoomAdminRestServlet(RestServlet):
             if not admin_users:
                 raise SynapseError(400, "No local admin user in room")
 
-            admin_user_id = admin_users[-1]
+            admin_user_id = None
+
+            for admin_user in reversed(admin_users):
+                if room_state.get((EventTypes.Member, admin_user)):
+                    admin_user_id = admin_user
+                    break
+
+            if not admin_user_id:
+                raise SynapseError(
+                    400, "No local admin user in room",
+                )
 
             pl_content = power_levels.content
         else:
@@ -499,3 +548,60 @@ class MakeRoomAdminRestServlet(RestServlet):
         )
 
         return 200, {}
+
+
+class ForwardExtremitiesRestServlet(RestServlet):
+    """Allows a server admin to get or clear forward extremities.
+
+    Clearing does not require restarting the server.
+
+        Clear forward extremities:
+        DELETE /_synapse/admin/v1/rooms/<room_id_or_alias>/forward_extremities
+
+        Get forward_extremities:
+        GET /_synapse/admin/v1/rooms/<room_id_or_alias>/forward_extremities
+    """
+
+    PATTERNS = admin_patterns("/rooms/(?P<room_identifier>[^/]*)/forward_extremities")
+
+    def __init__(self, hs: "HomeServer"):
+        self.hs = hs
+        self.auth = hs.get_auth()
+        self.room_member_handler = hs.get_room_member_handler()
+        self.store = hs.get_datastore()
+
+    async def resolve_room_id(self, room_identifier: str) -> str:
+        """Resolve to a room ID, if necessary."""
+        if RoomID.is_valid(room_identifier):
+            resolved_room_id = room_identifier
+        elif RoomAlias.is_valid(room_identifier):
+            room_alias = RoomAlias.from_string(room_identifier)
+            room_id, _ = await self.room_member_handler.lookup_room_alias(room_alias)
+            resolved_room_id = room_id.to_string()
+        else:
+            raise SynapseError(
+                400, "%s was not legal room ID or room alias" % (room_identifier,)
+            )
+        if not resolved_room_id:
+            raise SynapseError(
+                400, "Unknown room ID or room alias %s" % room_identifier
+            )
+        return resolved_room_id
+
+    async def on_DELETE(self, request, room_identifier):
+        requester = await self.auth.get_user_by_req(request)
+        await assert_user_is_admin(self.auth, requester.user)
+
+        room_id = await self.resolve_room_id(room_identifier)
+
+        deleted_count = await self.store.delete_forward_extremities_for_room(room_id)
+        return 200, {"deleted": deleted_count}
+
+    async def on_GET(self, request, room_identifier):
+        requester = await self.auth.get_user_by_req(request)
+        await assert_user_is_admin(self.auth, requester.user)
+
+        room_id = await self.resolve_room_id(room_identifier)
+
+        extremities = await self.store.get_forward_extremities_for_room(room_id)
+        return 200, {"count": len(extremities), "results": extremities}
diff --git a/synapse/rest/admin/users.py b/synapse/rest/admin/users.py
 index f39e3d6d5c..68c3c64a0d 100644
--- a/synapse/rest/admin/users.py
+++ b/synapse/rest/admin/users.py
@@ -83,17 +83,32 @@ class UsersRestServletV2(RestServlet):
     The parameter `deactivated` can be used to include deactivated users.
     """
 
-    def __init__(self, hs):
+    def __init__(self, hs: "HomeServer"):
         self.hs = hs
         self.store = hs.get_datastore()
         self.auth = hs.get_auth()
         self.admin_handler = hs.get_admin_handler()
 
-    async def on_GET(self, request):
+    async def on_GET(self, request: SynapseRequest) -> Tuple[int, JsonDict]:
         await assert_requester_is_admin(self.auth, request)
 
         start = parse_integer(request, "from", default=0)
         limit = parse_integer(request, "limit", default=100)
+
+        if start < 0:
+            raise SynapseError(
+                400,
+                "Query parameter from must be a string representing a positive integer.",
+                errcode=Codes.INVALID_PARAM,
+            )
+
+        if limit < 0:
+            raise SynapseError(
+                400,
+                "Query parameter limit must be a string representing a positive integer.",
+                errcode=Codes.INVALID_PARAM,
+            )
+
         user_id = parse_string(request, "user_id", default=None)
         name = parse_string(request, "name", default=None)
         guests = parse_boolean(request, "guests", default=True)
@@ -103,7 +118,7 @@ class UsersRestServletV2(RestServlet):
             start, limit, user_id, name, guests, deactivated
         )
         ret = {"users": users, "total": total}
-        if len(users) >= limit:
+        if (start + limit) < total:
             ret["next_token"] = str(start + len(users))
 
         return 200, ret
@@ -875,3 +890,39 @@ class UserTokenRestServlet(RestServlet):
         )
 
         return 200, {"access_token": token}
+
+
+class ShadowBanRestServlet(RestServlet):
+    """An admin API for shadow-banning a user.
+
+    A shadow-banned users receives successful responses to their client-server
+    API requests, but the events are not propagated into rooms.
+
+    Shadow-banning a user should be used as a tool of last resort and may lead
+    to confusing or broken behaviour for the client.
+
+    Example:
+
+        POST /_synapse/admin/v1/users/@test:example.com/shadow_ban
+        {}
+
+        200 OK
+        {}
+    """
+
+    PATTERNS = admin_patterns("/users/(?P<user_id>[^/]*)/shadow_ban")
+
+    def __init__(self, hs: "HomeServer"):
+        self.hs = hs
+        self.store = hs.get_datastore()
+        self.auth = hs.get_auth()
+
+    async def on_POST(self, request, user_id):
+        await assert_requester_is_admin(self.auth, request)
+
+        if not self.hs.is_mine_id(user_id):
+            raise SynapseError(400, "Only local users can be shadow-banned")
+
+        await self.store.set_shadow_banned(UserID.from_string(user_id), True)
+
+        return 200, {}
 |