The recent appearance of severe acute respiratory syndrome coronavirus (SARS–CoV) highlights the continual threat to human health posed by emerging viruses. However, the central processes in the evolution of emerging viruses are unclear, particularly the selection pressures faced by viruses in new host species. We outline some of the key evolutionary genetic aspects of viral emergence. We emphasize that, although the high mutation rates of RNA viruses provide them with great adaptability and explain why they are the main cause of emerging diseases, their limited genome size means that they are also subject to major evolutionary constraints. Understanding the mechanistic basis of these constraints, particularly the roles played by epistasis and pleiotropy, is likely to be central in explaining why some RNA viruses are more able than others to cross species boundaries. Viral genetic factors have also been implicated in the emergence of SARS–CoV, with the suggestion that this virus is a recombinant between mammalian and avian coronaviruses. We show, however, that the phylogenetic patterns cited as evidence for recombination are more probably caused by a variation in substitution rate among lineages and that recombination is unlikely to explain the appearance of SARS in humans.