It doesn't support ASP.NET Web Forms and ASP.NET MVC, but it supports ASP.NET Core MVC. It was announced that .NET Core 3 will support WPF and Windows Forms.
.NET Core contains a large subset of .NET Framework Base Class Library, with a different factoring (assembly names are different; members exposed on types differ in key cases). These differences require changes to port source to .NET Core in some cases
.NET Core implements a subset of the subsystems in the .NET Framework. For example, Code Access Security (CAS) is not supported, while reflection is supported.