This is in parts a survey talk about several recent results that relate the Casimir effect to spectral geometry and microlocal analysis. I will explain how the Casimir energy can be defined as the trace of an operator without the need for regularisation procedures. I will then give various recent results that allow to compute these quantities in terms of determinants of boundary layer operators in various geometric situations. If there is time I will also give some relations to wave-trace invariants.
(based on joint work with T. Betcke, F. Hanisch, Y.L. Fang, X. Sun, A. Waters)