Official app for OS X from Telegram team
This software is available under GPL v3 license.
Source code is available on GitHub.

Version history

v 0.10.16 19.10.16

  • New audio player design

Windows and Linux:

  • Quick reply from notifications
  • Hide all notifications button added
  • Change notifications location and maximum count

Windows 10:

  • Respecting quiet hours for the notifications

Linux:

  • You can enable native notifications in Settings

v 0.10 03.08.16

  • Trending stickers. Check out and install noteworthy sticker packs from the sticker packs settings box.
  • Archived stickers. Unused stickers are now archived automatically when you go over the 200 limit.
  • Group previews. Preview groups before joining them via invite link – see who else is in the group before joining.
  • New internal video player.
  • Improved design for chats.

v 0.9.56 26.06.16

  • Fixed photo viewer to handle screen resolution change correctly.
  • Fixed forwarding photos via drag-n-drop.
  • Various design improvements and other bug fixes.

v 0.9.50 14.06.16

  • Introducing Drafts: Seamless syncing for unsent messages on all your devices. Drafts are now visible in your chats list.
  • Completely redesigned group and user profiles.
  • Unread messages counter on the ‘Scroll to bottom’ button.

v 0.9.49 16.05.16

  • Edit your messages everywhere within 2 days after posting (press the up arrow button to edit your last message).
  • Mention people in groups by typing @ and selecting them from the list — even if they don't have a username.

v 0.9.41 11.04.16

  • Introducing Bot API 2.0, the biggest update to our bot platform since June 2015.
  • Bots can now update existing messages on the fly as you interact with them.
  • New Inline keyboards with callback, ‘open URL’ or ‘switch to inline mode’ buttons help create seamless interfaces.
  • Inline bots can now send all attachments supported by Telegram (videos, music, stickers, locations, etc.)

v 0.9.31 14.03.16

  • Supergroups can now have 5,000 members (up from 1,000).
  • Groups of any size may be converted to supergroups.
  • Make your supergroup public by setting up a public link – anyone will be able to view the chat and join it.
  • Pin messages to keep important updates visible and notify all members.
  • Select messages to delete, report as spam, block users, or remove all messages from a user.

v 0.9.28 26.02.16

  • Edit your messages in channels and supergroups.
  • Share links to specific posts in channels via the post context menu.
  • Add admin signatures to messages in channels.
  • Send silent messages in channels that will not notify members, useful for non-urgent or late night posting.

v 0.9.26 22.02.16

  • Adaptive layout for wide screens switch added to Settings.
  • Linux version crash fix.

v 0.9.24 16.02.16

  • New waveform visualizations for voice messages.
  • Sticker suggestions when you type an emoji.

v 0.9.16 04.01.16

  • GIFs autoplay and automatic download.
  • Inline bots support.
  • Automatic download settings added.
  • All media redesigned.

v 0.9.15 09.12.15

  • Sticker management: manually rearrange your sticker packs, pack order is now synced across all your devices.
  • Click and hold on a sticker to preview it before sending.
  • New context menu for chats in chats list.
  • Support for all existing emoji.

v 0.9.13 25.11.15

  • Groups can now have multiple administrators with the ability to edit the name and logo, and add and remove members.
  • Groups that have reached their capacity of 200 users can be upgraded to supergroups of up to 1,000 members.

v 0.9.10 04.11.15

  • New shared audio files section.
  • New design for popup menus.
  • Add captions to any photos you send.
  • Surround text with `single backticks` for inline monowidth code and ```triple backticks``` for blocks of code.
  • The Tilde symbol is now displayed correctly.

Alpha version

If you would like to get all updates faster and be the first to test new features, you are welcome to use Telegram Desktop's alpha version instead of the stable one.

The stable version is updated less frequently, but is tested better than the alpha version.

Here are the alpha version links for different platforms:

Windows Setup
Windows Portable
Mac OS X 10.8+ Setup
Mac OS X 10.6 and 10.7 Setup
Linux 64 bit
Linux 32 bit

Just install it on top of your current Telegram Desktop and there you go.
Your feedback is welcome on Twitter