Set estimation has to do with the statistical reconstruction of sets from random set of points. This theory is closely related with nonparametric functional estimation as well as with stochastic geometry. A nonexhaustive expository overview of set estimation theory is given. The aim is to present the basic ideas, some typical tools involved in the theory and a few applications. Most technicalities are omitted or summarized.

Keywords: Support estimation, level set estimation, boundary estimation.

AMS Subject classifications: 62G07, 62G20.