Astrocladistics, a methodology borrowed from biology, is an objective way of understanding galaxy diversity through evolutionary relationships. It is based on the evolution of all the available parameters describing galaxies and thus integrates the complexity of these objects. Through the formalization of the concepts around galaxy formation and evolution, and the identification of the processes of diversification (build up, secular evolution, interaction, merging/accretion, sweeping/ejection), galaxy diversity can be expected to organize itself in a hierarchy. About 500 galaxies described by about 40 observables have now been analysed and several robust trees found. For instance, we show that the Dwarf Galaxies of the Local Group all derive from a common ancestral kind of objects. We identify three evolutionary groups, each one having its own characteristics and own evolution. The Virgo galaxies present a relatively regular diversification, with rather few violent events such as major mergers. Diversification in another sample made of gas-poor galaxies in different environments appears to be slightly more complicated with several diverging evolutionary groups. Work on a large sample of galaxies at non-zero redshifts is in progress and is pioneering a brand new approach to exploit data from the big extragalactic surveys.