Explore a comprehensive lecture on the Casimir effect and its relation to spectral geometry and microlocal analysis. Delve into the definition of Casimir energy as an operator trace without the need for regularization procedures. Examine recent results that allow for the computation of these quantities using determinants of boundary layer operators in various geometric situations. Learn about the potential connections to wave-trace invariants. This 46-minute talk, presented by Alexander Strohmaier at the Workshop on "Spectral Theory of Differential Operators in Quantum Theory" held at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI), offers insights into joint work with T. Betcke, F. Hanisch, Y.L. Fang, X. Sun, and A. Waters.