The axolotl is one of the few tetrapods that are capable of regenerating complicated biological structures, such as complete limbs, throughout adulthood. Upon injury the axolotl generates a population of regeneration-competent limb progenitor cells known as the blastema, which will grow, establish pattern, and differentiate into the missing limb structures. In this review we focus on the crucial early events that occur during wound healing, the neural-epithelial interactions that drive the formation of the early blastema, and how these mechanisms differ from those of other species that have restricted regenerative potential, such as humans. We also discuss how the presence of cells from the different axes of the limb is required for the continued growth and establishment of pattern in the blastema as described in the polar coordinate model, and how this positional information is reprogrammed in blastema cells during regeneration. Multiple cell types from the mature limb stump contribute to the blastema at different stages of regeneration, and we discuss the contribution of these types to the regenerate with reference to whether they are "pattern-forming" or "pattern-following" cells. Lastly, we explain how an engineering approach will help resolve unanswered questions in limb regeneration, with the goal of translating these concepts to developing better human regenerative therapies.