Shape and material effects in Casimir forces

Casimir forces depend non-trivially on shape and material properties. Using ideas from electromagnetic scattering theory and conformal mappings, we have derived a number of novel analytical and numerical results for Casimir interactions. We shall give a brief overview of the general approach and present explicit results for some generic examples, including short- and long-distance expansions, interaction of perfect conductors with sharp edges and tips, and exact solutions in two and three dimensions. The predictions are compared to recent experiments.