The principles underlying regeneration in planarians have been explored for over 100 years through surgical manipulations and cellular observations. Planarian regeneration involves the generation of new tissue at the wound site via cell proliferation (blastema formation), and the remodeling of pre-existing tissues to restore symmetry and proportion (morphallaxis). Because blastemas do not replace all tissues following most types of injuries, both blastema formation and morphallaxis are needed for complete regeneration. Here we discuss a proliferative cell population, the neoblasts, that is central to the regenerative capacities of planarians. Neoblasts may be a totipotent stem-cell population capable of generating essentially every cell type in the adult animal, including themselves. The population properties of the neoblasts and their descendants still await careful elucidation. We identify the types of structures produced by blastemas on a variety of wound surfaces, the principles guiding the reorganization of pre-existing tissues, and the manner in which scale and cell number proportions between body regions are restored during regeneration.