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We give a short review on the static and dynamical Casimir effects, recallingtheir historical prediction, as well as their more recent experimentalverification. We emphasise on the central role played by so-called {\itdynamical boundary conditions} (for which the boundary condition depends on asecond time derivative of the field) in the experimental verification of thedynamical Casimir effect by Wilson et al. We then go on to review our previouswork on the static Casimir effect with dynamical boundary conditions, providingan overview on how to compute the so-called local Casimir energy, the totalCasimir energy and the Casimir force. We give as a future perspective thedirection in which this work should be generalised to put the theoreticalpredictions of the dynamical Casimir effect experiments on a rigorous footing.

A short review of the Casimir effect with emphasis on dynamical boundary conditions