Appears in collections : 19th workshop on stochastic geometry, stereology and image analysis / 19ème conférence en géométrie stochastique, stéréologie et analyse d'images, Exposés de recherche

A survey on some developments in curvature theory for random sets will be given. We first consider previous models with classical singularities like polyconvex sets or unions of sets with positive reach. The main part of the talk concerns extensions to certain classes of random fractals which have been investigated in the last years. In these cases limits of rescaled versions for suitable approximations are used.