In the early 1930s, the synthesis of Darwinian natural selection, mutation, and Mendelian genetics gave rise to the paradigm of ‘modern Darwinism’, also known as ‘neo-Darwinism’. This has contributed greatly to our understanding. But increasing knowledge of other mechanisms, including endosymbiosis, genetic and genomic duplication, polyploidy, hybridization, epigenetics, horizontal gene transfer in prokaryotes, and the modern synthesis of embryonic development and evolution, has widened our horizons to a diversity of possibilities for change. All of these can be gathered under the umbrella concept of ‘genomic creativity’, which, in partnership with natural selection, affords a more comprehensive modern explanation of evolution. © 2006 The Linnean Society of London, Biological Journal of the Linnean Society, 2006, 88, 655–672.