of Physics [@NJP06].

Meanwhile, it has been realized that the Casimir force was a dominant force at micron or sub-micron distances, and then clearly an important aspect in the domain of micro- and nano-oscillators (MEMS, NEMS) [@BuksPRB2001; @ChanScience2001; @ChanPRL2001] now emerging from modern nanofabrication techniques [@EkinciRSI2005]. If the Casimir force has been primarly considered as a source of stiction between mobile parts, it is now recognized as an essential source of actuation to be used in the design of MEMS and NEMS.

In both fundamental and technological contexts, it is extremely important to take into account the real experimental situations which largely differ from the ideal conditions considered by Casimir. We review below some theoretical tools which have shown their efficiency for a general formulation of the Casimir effect, accounting for the material properties of the interacting plates as well as for the effect of non planar boundary geometries.

Idealized Casimir force {#sec:1}
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The Casimir force and energy between two perfectly reflecting, plane and parallel mirrors immersed in quantum vacuum have the following forms $$\begin{aligned}
F_{\rm Cas} = \frac{\pi^{2}\hbar c}{240}\frac{A}{L^{4}}  \ \ , \ \
E_{\rm Cas} = - \frac{\pi^{2}\hbar c}{720}\frac{A}{L^{3}}.    \label{FEcas}\end{aligned}$$ These expressions correspond to an attractive force 