ASP.NET Core support in Visual Studio 2015?

Visual Studio 2015 will only support .NET Core <= 1.1 (ie. project.json). If you wish to use .csproj based .NET Core projects you will need to use Visual Studio 2017. You can read about the .NET Core Roadmap here.

You can stick with project.json and Visual Studio 2015. But if you want to move to .NET Core 2.0 you will need to open your project with Visual Studio 2017 which can migrate it to the new .csproj format. You can read about the migration process in this blog post.

Visual Studio 2017 will also provide stable RTM tooling for .NET Core 1.0 (note that the tooling in Visual Studio 2015 is only in preview). There is another interesting blog post here which discusses the move to the new project format, Joe Morris from Microsoft confirms there are no plans to have VS 2015 support the build/project system.

Update

With the release of Visual Studio 2019, the latest .NET Core SDKs are not supported in Visual Studio 2015 or 2017. Here is the compatibility matrix: