Planarians have a long history in the fields of developmental and regenerative biology. These animals have also sparked interest in neuroscience due to their neuroanatomy, spectrum of simple behaviors, and especially, their almost unparalleled ability to generate new neurons after any type of injury. Research in adult planarians has revealed that neuronal subtypes homologous to those found in vertebrates are generated from stem cells throughout their lives. This feat is recapitulated after head amputation, wherein animals are capable of regenerating whole brains and regaining complete neural function. In this review, we summarize early studies on the anatomy and function of the planarian nervous system and discuss our present knowledge of the molecular mechanisms governing neurogenesis in planarians. Modern studies demonstrate that the transcriptional programs underlying neuronal specification are conserved in these remarkable organisms. Thus, planarians are outstanding models to investigate questions about how stem cells can replace neurons in vivo. WIREs Dev Biol 2017, 6:e266. doi: 10.1002/wdev.266 For further resources related to this article, please visit the WIREs website.