Heritable variation between members of a population is normally attributed to genetic variation. Genes affecting important traits may be present or absent in different individuals or they may have DNA mutations affecting their expression or the properties of the encoded protein. However, there are examples of heritable variation that are not associated with changes to the sequence of DNA. Plants with differences in flower shape or fruit colour, for example, may have the same DNA sequence. I will describe recent research with plants that is unravelling the molecular basis of these epigenetic phenomena and its implications for agriculture and evolution.