You can run .NET Core on OS X[1] (and Linux, FreeBSD and Windows). There are plenty of rough edges still, but we're adding more functionality and making it more capable each day. Soon enough, all the .NET Core ports will be just as capable as the Windows version.
ASP.NET 5 still runs Mono by default on OS X, but you can switch to .NET Core with the DNVM tool [2].
Note the blog post from yesterday by the F# team on F# 4. [3]
There are some hello world examples in the repo listed above as well.
If you'd like, you can develop with the recently announced Visual Studio Code, announced ~yesterday.
I think this is still Mono, but full MSFT support of *Nix is said to be underway.
Also, if you use Yeoman, make sure you upgrade your aspnet generator. I had issues until I realized the version I had was generating a project with out of date dependencies.