The compositional evolution of vertebrate genomes is characterized: (i) by one predominant conservative mode, in which nucleotide changes occur, but the base composition of DNA sequences in general, and of coding sequences in particular, does not change; and (ii) by three different shifting or transitional modes, in which nucleotide changes are accompanied by changes in the base composition of sequences. Investigations on these evolutionary modes have shed new light on a central problem in molecular evolution, namely the role played by natural selection in modulating the mutational input. This review will present first the intragenomic shifts, the 'major shifts' and the 'minor shift', and then the 'whole-genome', or 'horizontal', shift. In each case, the shifts were preceded and followed by a conservative mode of evolution. This review expands on a previous one [Bernardi, Gene 241 (2000) 3-17], and summarizes the evidence that the changes of the compositional patterns of the genome and their maintenance are controlled by Darwinian natural selection.