Approximately 2 million people have had limb amputations in the United States due to disease or injury, with more than 185,000 new amputations every year. The ability to promote epimorphic regeneration, or the regrowth of a biologically based digit or limb, would radically change the prognosis for amputees. This ambitious goal includes the regrowth of a large number of tissues that need to be properly assembled and patterned to create a fully functional structure. We have yet to even identify, let alone address, all the obstacles along the extended progression that limit epimorphic regeneration in humans. This review aims to present introductory fundamentals in epimorphic regeneration to facilitate design and conduct of research from a tissue engineering and regenerative medicine perspective. We describe the clinical scenario of human digit healing, featuring published reports of regenerative potential. We then broadly delineate the processes of epimorphic regeneration in nonmammalian systems and describe a few mammalian regeneration models. We give particular focus to the murine digit tip, which allows for comparative studies of regeneration-competent and regeneration-incompetent outcomes in the same animal. Finally, we describe a few forward-thinking opportunities for promoting epimorphic regeneration in humans.