Adult neurogenesis, the generation of functional neurons from adult neural stem cells in the central nervous system (CNS), is widespread, and perhaps universal, among vertebrates. This phenomenon is more pronounced in teleost fish than in any other vertebrate taxon. There are up to 100 neurogenic sites in the adult teleost brain. New cells, including neurons and glia, arise from neural stem cells harbored both in neurogenic niches and outside these niches (such as the ependymal layer and parenchyma in the spinal cord, respectively). At least some, but not all, of the stem cells are of astrocytic identity. Aging appears to lead to stem cell attrition in fish that exhibit determinate body growth but not in those with indeterminate growth. At least in some areas of the CNS, the activity of the neural stem cells results in additive neurogenesis or gliogenesis – tissue growth by net addition of cells. Mathematical and computational modeling has identified three factors to be crucial for sustained tissue growth and correct formation of CNS structures: symmetric stem cell division, cell death and cell drift due to population pressure. It is hypothesized that neurogenesis in the CNS is driven by continued growth of corresponding muscle fibers and sensory receptor cells in the periphery to ensure a constant ratio of peripheral versus central elements. This ‘numerical matching hypothesis’ can explain why neurogenesis has ceased in most parts of the adult CNS during the evolution of mammals, which show determinate growth.