We give an overview of the work done during past ten years on Casimir interaction in electronic topological materials, our focus being solids, which possess surface or bulk band structures with nontrivial topologies, can be evinced through optical properties that are characterizable terms nonzero invariants. The examples we review three-dimensional magnetic insulators, two-dimensional Chern gra...

Taking the Mirabelli-Peskin model, we examine the Casimir effect in the brane world. It is compared with that of the ordinary Kaluza-Klein theory.