I am learning ASP.NET MVC and many concepts of “ASP.NET” like authentication, authorization, session state still apply to it.
But from whatever little I have understood, I don’t see that ViewState is still relevant in an ASP.NET application. But it is there (property of System.Web.Mvc.ViewPage)! Is it there only for compatibility reasons or it still have some purpose/use?
Yes, that is correct. ViewState is not relevant. More on differencies between Page Model and MVC here:
Compatibility of ASP.NET Web Forms and ASP.NET MVC