Understanding the factors that determine the rate at which genomes generate and fix mutations provides important insights into key evolutionary mechanisms. We review our current knowledge of the rates of mutation and substitution, as well as their determinants, in RNA viruses, DNA viruses and retroviruses. We show that the high rate of nucleotide substitution in RNA viruses is matched by some DNA viruses, suggesting that evolutionary rates in viruses are explained by diverse aspects of viral biology, such as genomic architecture and replication speed, and not simply by polymerase fidelity.