  We present calculations of the quantum and thermal Casimir interaction
between real mirrors in electromagnetic fields using the scattering approach.
We begin with a pedagogical introduction of this approach in simple cases where
the scattering is specular. We then discuss the more general case of stationary
arbitrarily shaped mirrors and present in particular applications to two
geometries of interest for experiments, that is corrugated plates and the
plane-sphere geometry. The results nicely illustrate the rich correlations
existing between material properties, temperature and geometry in the Casimir
effect.
