Regeneration is a remarkable phenomenon that has been the subject of awe and bafflement for hundreds of years. Although regeneration competence is found in highly divergent organisms throughout the animal kingdom, recent advances in tools used for molecular and genomic characterization have uncovered common genes, molecular mechanisms, and genomic features in regenerating animals. In this review we focus on what is known about how genome regulation modulates cellular potency during regeneration. We discuss this regulation in the context of complex tissue regeneration in animals, from Hydra to humans, with reference to ex vivo-cultured cell models of pluripotency when appropriate. We emphasize the importance of a detailed molecular understanding of both the mechanisms that regulate genomic output and the functional assays that assess the biological relevance of such molecular characterizations.