I'm taking a look at Visual Studio 2013 Browser Link and it seems like there should be other options for the connected browsers, like Design Mode and Inspect Mode. But for me, it's just showing Refresh.
I'm using VS 2013 with update 2. The project is an ASP.NET MVC application, with .NET 4.5 and debug is enabled in the web.config file.
Is there something I'm missing?
You need http://vswebessentials.com/download. Vs2013 alone will show only refresh action. All additional things are various extensions bundled as part of webessentials.