  We start this paper with a historical survey of the Casimir effect, showing
that its origin is related to experiments on colloidal chemistry. We present
two methods of computing Casimir forces, namely: the global method introduced
by Casimir, based on the idea of zero-point energy of the quantum
electromagnetic field, and a local one, which requires the computation of the
energy-momentum stress tensor of the corresponding field. As explicit examples,
we calculate the (standard) Casimir forces between two parallel and perfectly
conducting plates and discuss the more involved problem of a scalar field
submitted to Robin boundary conditions at two parallel plates. A few comments
are made about recent experiments that undoubtedly confirm the existence of
this effect. Finally, we briefly discuss a few topics which are either
elaborations of the Casimir effect or topics that are related in some way to
this effect as, for example, the influence of a magnetic field on the Casimir
effect of charged fields, magnetic properties of a confined vacuum and
radiation reaction forces on non-relativistic moving boundaries.
