Although polyploidy has been involved in speciation in both animals and plants, the general perception is often that it is too rare to have been a significant factor in animal evolution and its role in plant diversification has been questioned. These views have resulted in a bias towards explanations for what deters polyploidy, rather than the somewhat more interesting question of the mechanisms by which polyploidy arises and becomes established in both plants and animals. The evidence for and against some of the traditional views on polyploidy is reviewed, with an attempt to synthesize factors promoting evolution through genome duplication in both groups. It is predicted that polyploidy should be more common in temperate than in tropical breeders because environmental fluctuations may promote unreduced gamete formation, it should be most common in organisms with sufficient numbers of gametes that random meiotic problems can be overcome, and it should be more frequent when mechanisms to promote assortative mating are a direct byproduct of genome duplication. © 2004 The Linnean Society of London, Biological Journal of the Linnean Society, 2004, 82, 453–466.