Despite the remarkable unity of the basic components of the living world (DNA, RNA, the genetic code), we are probably still not aware of the diversity of genome structures nor of the diversity of means genomes use to evolve. Rearrangements, gene transfers, duplications, transposable elements, single nucleotide substitutions, repetitions, insertions, deletions, have been successively discovered and modeled in the XXth century. They are used to document the evolutionary history of life on earth and to understand adaptation processes.