I will discuss "bordered Floer homology", an invariant for three-manifolds with parameterized boundary. The theory associates a differential graded algebra to a (parameterized) surface; and a module over that algebra to a three-manifold which bounded by the surface. I will describe this construction, and then focus on computational aspects of this theory, including an algorithm for calculating HF-hat of closed three-manifolds, obtained by factoring mapping classes. This is joint work with Robert Lipshitz and Dylan Thurston.