The determination of populations is widespread in astrophysics. Classically at least three populations of stars are distinguished in galaxies, corresponding to different ages. It is now recognized that globular clusters contain more than one population or generation of stars. For galaxies, populations may be distinguished by their environment, their morphology or also by their redshift which leads to the notion of progenitors. But populations can also be identified as families or sub-classes, like Cepheids 1 and 2, or SNIa among supernovae. In any case, identifying populations is a process of classification. There are several methods that can yield different results, and the selection of the parameters is always crucial : it is not because an observable is both available and a priori astrophysically informative that it is statistically discriminant enough to partition the sample. An interesting contraint is that most often in astrophysics, the populations evolve as well as the individuals within each populations. I will review some of the issues with the statistical clustering of astrophysical objects in a multi-parameter space using examples with stars, GRBs, globular clusters and galaxies.