Teleost fish are distinguished by their ability to constitutively generate new neurons in the adult central nervous system (‘adult neurogenesis’), and to regenerate whole neurons after injury (‘neuronal regeneration’). In the brain, new neurons are produced in large numbers in several dozens of proliferation zones. In the spinal cord, proliferating cells are present in the ependymal layer and throughout the parenchyma. In the retina, new cells arise from the ciliary marginal zone and from Müller glia. Experimental evidence has suggested that both radial glia and non-glial cells can function as adult stem cells. The proliferative activity of these cells can be regulated by molecular factors, such as fibroblast growth factor and Notch, as well as by social and behavioral experience. The young cells may either reside near the respective proliferation zone, or migrate to specific target areas. Approximately half of the newly generated cells persist for the rest of the fish’s life, and many of them differentiate into neurons. After injury, a massive surge of apoptotic cell death occurs at the lesion site within a few hours. Apoptosis is followed by a marked increase in cell proliferation and neurogenesis, leading to repair of the tissue. The structural regeneration is paralleled by partial or complete recovery of function. Recent investigations have led to the identification of several dozens of molecular factors that are potentially involved in the process of regeneration.