Nowadays, one of the leading causes of death in humans is cancer, which is still on the rise globally and is in great need of intense study on the pathogenic mechanism and effective therapy. Epigenetics is a discipline that studies heritable changes in gene expression without alteration of DNA sequence. Epigenetic changes mainly involve DNA methylation, histone modifications and non-coding RNA (ncRNA) expression, which are interconnected to play a crucial role in the initiation and progression of various malignancies. Curcumin is a type of plant-derived polyphenolic compound with strong bioactivity against various disorders, particularly cancer. Retrieving commonly used databases such as PubMed, Google Scholar and CNKI, we summarized recent advances in the efficacy of curcumin on cancer and its epigenetic regulation in terms of DNA methylation, histone modifications and ncRNA expression. Furthermore, we also focused on improving the bioavailability of curcumin by development of novel curcumin analogs with high bioavailability, nanoparticles-loaded drug delivery system for curcumin, and combination therapy of curcumin with other agents. This review provides comprehensive insights into the molecular mechanisms, on the basis of epigenetic regulation, underlying the clinical application of curcumin in cancer.