Active set algorithms, such as the projected gradient method in nonlinear optimization, are designed to "identify'' the active constraints of the problem in a finite number of iterations. Using the notions of "partial smoothness'' and "prox-regularity'' we extend work of Burke, Morée and Wright on identifiable surfaces from the convex case to a general nonsmooth setting. We further show how this setting can be used in the study of sufficient conditions for local minimizers.