  We give a short review on the static and dynamical Casimir effects, recalling
their historical prediction, as well as their more recent experimental
verification. We emphasise on the central role played by so-called {\it
dynamical boundary conditions} (for which the boundary condition depends on a
second time derivative of the field) in the experimental verification of the
dynamical Casimir effect by Wilson et al. We then go on to review our previous
work on the static Casimir effect with dynamical boundary conditions, providing
an overview on how to compute the so-called local Casimir energy, the total
Casimir energy and the Casimir force. We give as a future perspective the
direction in which this work should be generalised to put the theoretical
predictions of the dynamical Casimir effect experiments on a rigorous footing.
