Myxoma virus (MYXV) is the type species of the Leporipoxviruses, a genus of Chordopoxvirinae, double stranded DNA viruses, whose members infect leporids and squirrels, inducing cutaneous fibromas from which virus is mechanically transmitted by biting arthropods. However, in the European rabbit (Oryctolagus cuniculus), MYXV causes the lethal disease myxomatosis. The release of MYXV as a biological control for the wild European rabbit population in Australia, initiated one of the great experiments in evolution. The subsequent coevolution of MYXV and rabbits is a classic example of natural selection acting on virulence as a pathogen adapts to a novel host species. Slightly attenuated mutants of the progenitor virus were more readily transmitted by the mosquito vector because the infected rabbit survived longer, while highly attenuated viruses could be controlled by the rabbit immune response. As a consequence, moderately attenuated viruses came to dominate. This evolution of the virus was accompanied by selection for genetic resistance in the wild rabbit population, which may have created an ongoing co-evolutionary dynamic between resistance and virulence for efficient transmission. This natural experiment was repeated on a continental scale with the release of a separate strain of MYXV in France and its subsequent spread throughout Europe. The selection of attenuated strains of virus and resistant rabbits mirrored the experience in Australia in a very different environment, albeit with somewhat different rates. Genome sequencing of the progenitor virus and the early radiation, as well as those from the 1990s in Australia and Europe, has shown that although MYXV evolved at high rates there was no conserved route to attenuation or back to virulence. In contrast, it seems that these relatively large viral genomes have the flexibility for multiple pathways that converge on a similar phenotype.