Computational scientists have developed algorithms inspired by natural evolution for at least 50 years. These algorithms solve optimization and design problems by building solutions that are 'more fit' relative to desired properties. However, the basic assumptions of this approach are outdated. We propose a research programme to develop a new field: computational evolution. This approach will produce algorithms that are based on current understanding of molecular and evolutionary biology and could solve previously unimaginable or intractable computational and biological problems.