ABSTRACT: Shape From Shading  is the process of  computing the three-dimensional shape of  a surface from one image of that surface. Contrary to most of the other three-dimensional reconstruction problems (for example, stereo and photometric stereo),   in the Shape From Shading problem, data are minimal (we use a single image!).  As a consequence, this inverse problem is intrinsically a difficult one. In this chapter we describe the main difficulties of the problem and the most recent theoretical results. We also give some examples of realistic modelings and of rigorous numerical methods.