diff --git a/telethon/_client/telegrambaseclient.py b/telethon/_client/telegrambaseclient.py
index b6872dc8..5c32d086 100644
--- a/telethon/_client/telegrambaseclient.py
+++ b/telethon/_client/telegrambaseclient.py
@@ -91,6 +91,7 @@ def init(
         request_retries: int = 4,
         flood_sleep_threshold: int = 60,
         # Update handling.
+        catch_up: bool = False,
         receive_updates: bool = True,
         max_queued_updates: int = 100,
 ):
@@ -142,6 +143,7 @@ def init(
     self._parse_mode = markdown
 
     # Update handling.
+    self._catch_up = catch_up
     self._no_updates = not receive_updates
     self._updates_queue = asyncio.Queue(maxsize=max_queued_updates)
     self._updates_handle = None
@@ -232,6 +234,8 @@ async def connect(self: 'TelegramClient') -> None:
         )
     else:
         try_fetch_user = self._session_state.user_id == 0
+        if self._catch_up:
+            self._message_box.load(self._session_state, await self._session.get_all_channel_states())
 
     dc = all_dcs.get(self._session_state.dc_id)
     if dc is None:
@@ -358,6 +362,15 @@ async def _disconnect(self: 'TelegramClient'):
     except asyncio.CancelledError:
         pass
 
+    await self._session.insert_entities(self._entity_cache.get_all_entities())
+
+    session_state, channel_states = self._message_box.session_state()
+    for channel_id, pts in channel_states.items():
+        await self._session.insert_channel_state(channel_id, pts)
+
+    await self._replace_session_state(**session_state)
+
+
 async def _switch_dc(self: 'TelegramClient', new_dc):
     """
     Permanently switches the current connection to the new data center.
diff --git a/telethon/_sessions/sqlite.py b/telethon/_sessions/sqlite.py
index 2ea419be..b41975fb 100644
--- a/telethon/_sessions/sqlite.py
+++ b/telethon/_sessions/sqlite.py
@@ -245,7 +245,7 @@ class SQLiteSession(Session):
         try:
             c.executemany(
                 'insert or replace into entity values (?,?,?)',
-                [(e.id, e.access_hash, e.ty) for e in entities]
+                [(e.id, e.access_hash, e.ty.value) for e in entities]
             )
         finally:
             c.close()
diff --git a/telethon/_updates/entitycache.py b/telethon/_updates/entitycache.py
index 176d2013..ce89eb4f 100644
--- a/telethon/_updates/entitycache.py
+++ b/telethon/_updates/entitycache.py
@@ -95,3 +95,6 @@ class EntityCache:
             for c in chats
             if getattr(c, 'access_hash', None) and not getattr(c, 'min', None)
         )
+
+    def get_all_entities(self):
+        return [Entity(ty, id, hash) for id, (hash, ty) in self.hash_map.items()]
diff --git a/telethon/_updates/messagebox.py b/telethon/_updates/messagebox.py
index 235247f3..232ef446 100644
--- a/telethon/_updates/messagebox.py
+++ b/telethon/_updates/messagebox.py
@@ -141,46 +141,38 @@ class MessageBox:
 
     # region Creation, querying, and setting base state.
 
-    @classmethod
-    def load(cls, session_state, channel_states):
+    def load(self, session_state, channel_states):
         """
         Create a [`MessageBox`] from a previously known update state.
         """
         deadline = next_updates_deadline()
-        return cls(
-            map={
-                ENTRY_ACCOUNT: State(pts=session_state.pts, deadline=deadline),
-                ENTRY_SECRET: State(pts=session_state.qts, deadline=deadline),
-                **{s.channel_id: s.pts for s in channel_states}
-            },
-            date=session_state.date,
-            seq=session_state.seq,
-            next_deadline=ENTRY_ACCOUNT,
-        )
+        self.map = {
+            ENTRY_ACCOUNT: State(pts=session_state.pts, deadline=deadline),
+            ENTRY_SECRET: State(pts=session_state.qts, deadline=deadline),
+            **{s.channel_id: State(pts=s.pts, deadline=deadline) for s in channel_states}
+        }
+        self.date = session_state.date
+        self.seq = session_state.seq
+        self.next_deadline = ENTRY_ACCOUNT
 
-    @classmethod
     def session_state(self):
         """
-        Return the current state in a format that sessions understand.
+        Return the current state.
 
         This should be used for persisting the state.
         """
-        return SessionState(
-            user_id=0,
-            dc_id=0,
-            bot=False,
-            pts=self.map.get(ENTRY_ACCOUNT, 0),
-            qts=self.map.get(ENTRY_SECRET, 0),
+        return dict(
+            pts=self.map[ENTRY_ACCOUNT].pts if ENTRY_ACCOUNT in self.map else 0,
+            qts=self.map[ENTRY_SECRET].pts if ENTRY_SECRET in self.map else 0,
             date=self.date,
             seq=self.seq,
-            takeout_id=None,
-        ), [ChannelState(channel_id=id, pts=pts) for id, pts in self.map.items() if isinstance(id, int)]
+        ), {id: state.pts for id, state in self.map.items() if isinstance(id, int)}
 
     def is_empty(self) -> bool:
         """
         Return true if the message box is empty and has no state yet.
         """
-        return self.map.get(ENTRY_ACCOUNT, NO_SEQ) == NO_SEQ
+        return ENTRY_ACCOUNT not in self.map or self.map[ENTRY_ACCOUNT] == NO_SEQ
 
     def check_deadlines(self):
         """
@@ -200,7 +192,7 @@ class MessageBox:
         if self.possible_gaps:
             deadline = min(deadline, *(gap.deadline for gap in self.possible_gaps.values()))
         elif self.next_deadline in self.map:
-            deadline = min(deadline, self.map[self.next_deadline])
+            deadline = min(deadline, self.map[self.next_deadline].deadline)
 
         if now > deadline:
             # Check all expired entries and add them to the list that needs getting difference.