ASP.NET Core is the new open source and cross-platform web application (MVC and web API) framework from Microsoft. You can now develop and deploy your web apps on Mac and Linux. However, it is evolving rapidly and it can be hard to to find stability. There are many ways to deal with these changes and there are some releases with long term support guarantees. It also helps to understand Microsoft's strategy and how .NET Core ties in with Xamarin, the new Visual Studio tooling and .NET Standard.
Video here: https://skillsmatter.com/skillscasts/9916-on-aspdot-net-core-and-moving-targets#video (looks like skills matter has some trouble with the A/V).