Cancer is a disease caused by a series of genetic and epigenetic alterations. Therefore, agents targeting the genetic and/or epigenetic machinery offer potential for the development of anticancer drugs. Accumulating evidence has demonstrated that some common natural products [such as epigallocatechin-3-gallate (EGCG), curcumin, genistein, sulforaphane (SFN) and resveratrol] have anticancer properties through the mechanisms of altering epigenetic processes [including DNA methylation, histone modification, chromatin remodeling, microRNA (miRNA) regulation] and targeting cancer stem cells (CSCs). These bioactive compounds are able to revert epigenetic alterations in a variety of cancers in vitro and in vivo. They exert anticancer effects by targeting various signaling pathways related to the initiation, progression and metastasis of cancer. It appears that natural products hold great promise for cancer prevention and treatment by altering various epigenetic modifications. This review aims to discuss our current understanding of genetic and epigenetic targets of natural products and the effects of some common natural products on cancer chemoprevention and treatment.