Where is Elixir gaining most of its traction with companies? What types of problems? I've seen the Phoenix web framework mentioned many times, for example:

http://www.phoenixframework.org/docs/overview

I'm using it to convert a rails app into a stateful websocket-based service. Honestly I'm barely using the Phoenix framework aside from the channels and potentially presence. (Which isn't a knock on Phoenix, which is awesome, has great documentation for the most part, a very helpful community) I expect I'll make more use of it at some point but if you treat your app as something deeper than basic CRUD this is where the stateful processes of BEAM really come in handy.

In another app that was green-field we're using it to build a highly scalable estimation engine, which is to say, a glorified calculator over a somewhat complex data model.

Elixir is great for anything that uses concurrency. We're using it at my company for logging, among other things.

I've mainly seen it discussed in the webdev community

Web/mobile backends in our limited experience