Knot Floer homology, developed by Ozsvath and Szabo and independently by Rasmussen, associates a sequence of graded abelian groups to a nullhomologous knot in a closed three-manifold, Y. When Y is S^3, the Euler characteristic of their invariant is the classical Alexander polynomial; hence, knot Floer homology has been able to provide more complete answers to some questions that the Alexander polynomial addresses only partially. For example, knot Floer homology detects the Seifert genus of a knot and provides better obstructions to a knot being fibered or slice. In my talk, I will discuss the knot Floer homology of the preimage of a knot inside its cyclic branched covers, focusing particular attention on the double-branched covers of two-bridge knots in S^3. These techniques may yield new obstructions to a knot being slice.