I have some unit test fixtures which have been attributed with [Category("Fast")] How to configure TeamCity so that it runs only the unit tests whose category name is "Fast"? I'm sure there must be a way.

When you are using the built-in NUnit build step you could specify the categories which should be tested and which not. <img src="https://i.stack.imgur.com/VmiAh.png" alt="enter image description here"> See http://confluence.jetbrains.com/display/TCD8/NUnit