Multivariate clustering in astrophysics is a recent development justified by the bigger and bigger surveys of the sky. The phylogenetic approach is probably the most unexpected technique that has appeared for the unsupervised classification of galaxies, stellar populations or globular clusters. On one side, this is a somewhat natural way of classifying astrophysical entities which are all evolving objects. On the other side, several conceptual and practical difficulties arize, such as the hierarchical representation of the astrophysical diversity, the continuous nature of the parameters, and the adequation of the result to the usual practice for the physical interpretation. Most of these have now been solved through the studies of limited samples of stellar clusters and galaxies. Up to now, only the Maximum Parsimony (cladistics) has been used since it is the simplest and most general phylogenetic technique. Probabilistic and network approaches are obvious extensions that should be explored in the future.