We hypothesize that heritable epigenetic changes can affect rates of fitness increase as well as patterns of genotypic and phenotypic change during adaptation. In particular, we suggest that when natural selection acts on pure epigenetic variation in addition to genetic variation, populations adapt faster, and adaptive phenotypes can arise before any genetic changes. This may make it difficult to reconcile the timing of adaptive events detected using conventional population genetics tools based on DNA sequence data with environmental drivers of adaptation, such as changes in climate. Epigenetic modifications are frequently associated with somatic cell differentiation, but recently epigenetic changes have been found that can be transmitted over many generations. Here, we show how the interplay of these heritable epigenetic changes with genetic changes can affect adaptive evolution, and how epigenetic changes affect the signature of selection in the genetic record.