The Hubble tuning fork diagram, based on morphology, has always been the preferred scheme for classification of galaxies and is still the only one originally built from historical/evolutionary relationships. At the opposite, biologists have long taken into account the parenthood links of living entities for classification purposes. Assuming branching evolution of galaxies as a "descent with modification", we show that the concepts and tools of phylogenetic systematics widely used in biology can be heuristically transposed to the case of galaxies. This approach that we call "astrocladistics" has been first applied to Dwarf Galaxies of the Local Group and provides the first evolutionary galaxy tree. The cladogram is sufficiently solid to support the existence of a hierarchical organization in the diversity of galaxies, making it possible to track ancestral types of galaxies. We also find that morphology is a summary of more fundamental properties. Astrocladistics applied to cosmology simulated galaxies can, unsurprisingly, reconstruct the correct "genealogy". It reveals evolutionary lineages, divergences from common ancestors, character evolution behaviours and shows how mergers organize galaxy diversity. Application to real normal galaxies is in progress. Astrocladistics opens a new way to analyse galaxy evolution and a path towards a new systematics of galaxies.