The ability of some organisms to regenerate parts of their body has fascinated scientists for decades. The process of regeneration depends on the potential of certain cells to proliferate and contribute to the formation of new tissue. Organisms have evolved two strategies by which to achieve this: the maintenance of adult stem cells and the induction of stem-cell properties in differentiated cells. In both cases, cells must undergo extensive epigenetic reprogramming to attain the specialized functions of the new tissue. Ultimately, the regenerative capacity of a tissue might depend on the plasticity of the cellular epigenome, which determines the ability of the cell to respond to injury-related signals. Understanding this epigenetic plasticity will allow the development of strategies to stimulate the regeneration of damaged tissues and organs in humans.