Phylogeny, be it morphological or molecular, has long tried to explain the extant biodiversity by the Tree of Species, which is a logical consequence of strict Darwinian evolutionary principles. Through constant improvement of both methods and data sets, some parts of this diversity have actually been demonstrated to be the result of a tree-like process. For some other parts, and especially for prokaryotes, different molecular markers have, however, produced different evolutionary trees, preventing the reconstruction of such a Tree. While technical artifacts could be blamed for these discrepancies, Lateral Gene Transfers are now largely held for responsible, and their existence requires an extension of the Darwinian framework, since genetic material is not always vertically inherited from parents to offspring. Through a variety of biological processes, sometimes large parts of DNA are exchanged between phylogenetically distant contemporary organisms, especially between those sharing the same environment. While mainly concerning prokaryotes, Lateral Gene Transfers have been also demonstrated to affect eukaryotes, and even multicellular ones, like plants or animals. Most of the time, these transfers allow important adaptations and the colonisation of new niches. The quantitative and qualitative importance of genetic transfers has thus severely challenged the very existence of a universal Tree of Species, since genetic connections, at least for microbes, seem more reticulated than tree-like. Even traditional biological concepts, like the concept of species, need to be re-evaluated in the light of recent discoveries. In short, instead of focusing on a elusive universal tree, biologists are now considering the whole forest corresponding to the multiple processes of inheritance, both vertical and horizontal. This constitutes the major challenge of evolutionary biology for the years to come.