Slow dynamics of stepped surfaces

Two kinds of configurations involving steps on surfaces are reviewed. The first one results from an initially planar vicinal surface, i.e. slightly deviating from a high-symmetry (001) or (111) orientation. In some cases, these surfaces separate into domains of different orientations by a mechanism which is very similar to phase separation in mixtures. The domain size initially increases with time and goes to a finite limit, whose value is related to elastic phenomena. The second kind of configurations results from making grooves in a high-symmetry surface. The surface smoothes out and takes an intermediate shape with facet-like hills and valleys, which are the source of a controversy which we try to clarify as much as possible.