We discuss the progress in realistic calculations of the optical response o
f semiconductor surfaces. It concerns numerical developments as well as the
better inclusion of many-body effects. We show that the starting point of
such calculations, the atomic structure and the surface equilibrium phase,
can be now derived with high accuracy. The different steps are described in
detail for the computation of the reflectance anisotropy and the explorati
on of the In-rich InP(001)2 x 4 surfaces.