Questions about how and why tissue regeneration occurs have captured the attention of countless biologists, biomedical engineers and clinicians. Regenerative capacity differs greatly across organs and organisms, and a range of model systems that use different regenerative strategies and that offer different technical advantages have been studied to understand regeneration. Making use of this range of systems and approaches, recent advances have allowed progress to be made in understanding several key issues that are common to natural regenerative events. These issues include: the determination of regenerative capacity; the importance of stem cells, dedifferentiation and transdifferentiation; how regenerative signals are initiated and targeted; and the mechanisms that control regenerative proliferation and patterning.