  We review the theory of the Casimir effect using scattering techniques. After
years of theoretical efforts, this formalism is now largely mastered so that
the accuracy of theory-experiment comparisons is determined by the level of
precision and pertinence of the description of experimental conditions. Due to
an imperfect knowledge of the optical properties of real mirrors used in the
experiment, the effect of imperfect reflection remains a source of uncertainty
in theory-experiment comparisons. For the same reason, the temperature
dependence of the Casimir force between dissipative mirrors remains a matter of
debate. We also emphasize that real mirrors do not obey exactly the assumption
of specular reflection, which is used in nearly all calculations of material
and temperature corrections. This difficulty may be solved by using a more
general scattering formalism accounting for non-specular reflection with
wavevectors and field polarizations mixed. This general formalism has already
been fruitfully used for evaluating the effect of roughness on the Casimir
force as well as the lateral Casimir force appearing between corrugated
surfaces. The commonly used `proximity force approximation' turns out to lead
to inaccuracies in the description of these two effects.
