Evolutionary changes in organismal traits may occur either gradually or suddenly. However, until recently, there has been little direct information about how phenotypic changes are related to the rate and the nature of the underlying genotypic changes. Technological advances that facilitate whole-genome and whole-population sequencing, coupled with experiments that 'watch' evolution in action, have brought new precision to and insights into studies of mutation rates and genome evolution. In this Review, we discuss the evolutionary forces and ecological processes that govern genome dynamics in various laboratory systems in the context of relevant population genetic theory, and we relate these findings to evolution in natural populations.