diff --git a/telethon/client/messages.py b/telethon/client/messages.py
index 6ec6ad24..7574142f 100644
--- a/telethon/client/messages.py
+++ b/telethon/client/messages.py
@@ -19,7 +19,7 @@ class _MessagesIter(RequestIter):
     """
     async def _init(
             self, entity, offset_id, min_id, max_id,
-            from_user, offset_date, add_offset, filter, search
+            from_user, offset_date, add_offset, filter, search, reply_to
     ):
         # Note that entity being `None` will perform a global search.
         if entity:
@@ -87,6 +87,18 @@ class _MessagesIter(RequestIter):
                 offset_id=offset_id,
                 limit=1
             )
+        elif reply_to is not None:
+            self.request = functions.messages.GetRepliesRequest(
+                peer=self.entity,
+                msg_id=reply_to,
+                offset_id=offset_id,
+                offset_date=offset_date,
+                add_offset=add_offset,
+                limit=1,
+                max_id=0,
+                min_id=0,
+                hash=0
+            )
         elif search is not None or filter or from_user:
             # Telegram completely ignores `from_id` in private chats
             ty = helpers._entity_type(self.entity)
@@ -236,7 +248,7 @@ class _MessagesIter(RequestIter):
             # (only for the first request), it's safe to just clear it off.
             self.request.max_date = None
         else:
-            # getHistory and searchGlobal call it offset_date
+            # getHistory, searchGlobal and getReplies call it offset_date
             self.request.offset_date = last_message.date
 
         if isinstance(self.request, functions.messages.SearchGlobalRequest):
@@ -325,7 +337,8 @@ class MessageMethods:
             from_user: 'hints.EntityLike' = None,
             wait_time: float = None,
             ids: 'typing.Union[int, typing.Sequence[int]]' = None,
-            reverse: bool = False
+            reverse: bool = False,
+            reply_to: int = None
     ) -> 'typing.Union[_MessagesIter, _IDsIter]':
         """
         Iterator over the messages for the given chat.
@@ -433,6 +446,26 @@ class MessageMethods:
 
                 You cannot use this if both `entity` and `ids` are `None`.
 
+            reply_to (`int`, optional):
+                If set to a message ID, the messages that reply to this ID
+                will be returned. This feature is also known as comments in
+                posts of broadcast channels, or viewing threads in groups.
+
+                This feature can only be used in broadcast channels and their
+                linked megagroups. Using it in a chat or private conversation
+                will result in ``telethon.errors.PeerIdInvalidError`` to occur.
+
+                When using this parameter, the ``filter`` and ``search``
+                parameters have no effect, since Telegram's API doesn't
+                support searching messages in replies.
+
+                .. note::
+
+                    This feature is used to get replies to a message in the
+                    *discussion* group. If the same broadcast channel sends
+                    a message and replies to it itself, that reply will not
+                    be included in the results.
+
         Yields
             Instances of `Message <telethon.tl.custom.message.Message>`.
 
@@ -459,6 +492,10 @@ class MessageMethods:
                 from telethon.tl.types import InputMessagesFilterPhotos
                 async for message in client.iter_messages(chat, filter=InputMessagesFilterPhotos):
                     print(message.photo)
+
+                # Getting comments from a post in a channel:
+                async for message in client.iter_messages(channel, reply_to=123):
+                    print(message.chat.title, message.text)
         """
         if ids is not None:
             if not utils.is_list_like(ids):
@@ -486,7 +523,8 @@ class MessageMethods:
             offset_date=offset_date,
             add_offset=add_offset,
             filter=filter,
-            search=search
+            search=search,
+            reply_to=reply_to
         )
 
     async def get_messages(self: 'TelegramClient', *args, **kwargs) -> 'hints.TotalList':