Epigenetics is the study of changes in gene activity that can be transmitted through cell divisions but cannot be explained by changes in the DNA sequence. Epigenetic mechanisms are central to gene regulation, phenotypic plasticity, development and the preservation of genome integrity. Epigenetic mechanisms are often held to make a minor contribution to evolutionary change because epigenetic states are typically erased and reset at every generation, and are therefore, not heritable. Nonetheless, there is growing appreciation that epigenetic variation makes direct and indirect contributions to evolutionary processes. First, some epigenetic states are transmitted intergenerationally and affect the phenotype of offspring. Moreover, bona fide heritable ‘epialleles' exist and are quite common in plants. Such epialleles could, therefore, be subject to natural selection in the same way as conventional DNA sequence-based alleles. Second, epigenetic variation enhances phenotypic plasticity and phenotypic variance and thus can modulate the effect of natural selection on sequence-based genetic variation. Third, given that phenotypic plasticity is central to the adaptability of organisms, epigenetic mechanisms that generate plasticity and acclimation are important to consider in evolutionary theory. Fourth, some genes are under selection to be ‘imprinted' identifying the sex of the parent from which they were derived, leading to parent-of-origin-dependent gene expression and effects. These effects can generate hybrid disfunction and contribute to speciation. Finally, epigenetic processes, particularly DNA methylation, contribute directly to DNA sequence evolution, because they act as mutagens on the one hand and modulate genome stability on the other by keeping transposable elements in check. This article is part of the theme issue ‘How does epigenetics influence the course of evolution?'