Recs.
Updated
SpecsUpdate
Pros
Pro Secure
Pro Save time with inline bots and link previews
Unfortunately on the desktop, videos don't apply, but images are viewable without visiting popular websites like imgur and Instagram.
You can play YouTube videos and others within the app, so you don't need the embed code or anything.
With inline bots, such as @gif, @pic/bing, @vid/YouTube, etc, you can look things up without leaving the client or chat that you're in. Simply type the name and some keywords and wait for the results to load.
Pro Many good looking sticker sets
Telegram has countless sticker sets available, and it is possible to design and upload your own stickers.
Pro 2-step verification
You can set up an additional password to your account, which can be reset by your email. You don't have to use an email, if you do not want to. If you lose access to your email or forget your password, you will be able to reset if via text message if you're account is over seven days old and will receive it within a week (in case you recover anything before then).
Pro Compelling story
The founder Pavel Durov was exiled from Russia after refusing to cooperate with the Kreml to stamp the opposition and oppress the people. He nearly lost everything he worked on and started Telegram in exile. He has been a big proponent of free speech and unquestioned privacy since then.
Pro Cloud chat key are kept in different jurisdiction
Even though encryption used for cloud based storage (e.g. Gmail, Facebook, iCloud) may not be as secure as end-to-end encryption or zero-knowledge storage, Telegram does the most that it can by holding keys to chats in different jurisdictions, requiring intergovernmental cooperation to obtain the keys. This is aside from whatever security measure are taken place, of course.
Pro Supergroups of up to 100,000 people
In Supergroups, anyone along with admins can delete their messages from all sides. A message can be pinned to the top. All of the user's messages can be deleted by an administrator, and they can be banned and reported as well. Supergroups can have a public link (outside of Asia, due to high spam volumes), which is also a username.
Pro Supergroups of up to 5000 people
In Supergroups, anyone along with admins can delete their messages from all sides. A message can be pinned to the top. All of the user's messages can be deleted by an administrator, and they can be banned and reported as well. Supergroups can have a public link (outside of Asia, due to high spam volumes), which is also a username.
Pro Two-step verification
You can set up an additional password to your account, which can be reset by your email. You don't have to use an email if you do not want to. If you lose access to your email or forget your password, you will be able to reset it via text message if your account is over seven days old and will receive it within a week (in case you recover anything before then).
Cons
Con Only "Secret Chat" messages are encrypted end to end
The only way to get end-to-end encryption (client-client) using Telegram is to use the Secret Chat function, anything through the service is server-client encrypted. Also secret chat is only implemented in the mobile apps, meaning there is no way to encrypt messages end-to-end when using the desktop client or the web browser client.
Con They suggest security which is sometimes not available
In the past, they suggested full encryption everywhere. They did not state, that their group chat is unencrypted, while it was the case. This means, highly critical content gets shared while both, users and content is easily trackable over network providers and through other sources.
Much governments literally hunt the people so this is highly critical and as you can see on the example of other issues here on the page, is Telegram USED to this kind of security standards.
So it is seriously possible, that they succeed doing so.
From that point of view is Telegram to be a complete no-go for critical communication while it contains a huge load of benefits on other sides.
Since the server side software is non-free in an addition, is not even a fork possible which one would be able to do it differently in security terms, so double thumbs down.
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Flagged Pros + Cons
Pro Free and convenient large file sharing
Copy/paste videos, gifs, images, geolocation, and documents, drag over files for practically any time up to 1.5GB in size. Images can be compressed, too.
Pro Cloud chat keys are kept in different jurisdiction
Even though encryption used for cloud-based storage (e.g. Gmail, Facebook, iCloud) may not be as secure as end-to-end encryption or zero-knowledge storage, Telegram does the most that it can by holding keys to chats in different jurisdictions, requiring intergovernmental cooperation to obtain the keys. This is aside from whatever other security measures have been taken, of course.
Pro Cross-platform
Has client for Linux, Windows, MacOS for desktop. Has Android, iOS, Windows Phone client for mobile. And has a web client for all of them.