The Hubble tuning fork diagram, based on morphology and established in the 1930s, has always been the preferred scheme for classification of galaxies. However, the current large amount of multiwavelength data, most often spectra, for objects up to very high distances, asks for more sophisticated statistical approaches. Interpreting formation and evolution of galaxies as a ‘transmission with modification' process, we have shown that the concepts and tools of phylogenetic systematics can be heuristically transposed to the case of galaxies. This approach, which we call ‘astrocladistics', has successfully been applied on several samples. Many difficulties still remain, some of them being specific to the nature of both galaxies and their diversification processes, some others being classical in cladistics, like the pertinence of the descriptors in conveying any useful evolutionary information.