We use websockets for pushing things like comments, answers and question edits as they are added as well as for notifications like inbox messages and reputation updates.

Our websocket process currently has ~500k concurrent connections across 9 web servers.

Nick has some information on his blog (https://nickcraver.com/blog/2016/02/17/stack-overflow-the-ar...) although it’s a little outdated - we no longer use Netgain, we use the .NET Core websockets bits instead.