At birth or after hatching from the egg, vertebrate brains still contain neural stem cells which reside in specialized niches. In some cases, these stem cells are deployed for further postnatal development of parts of the brain until the final structure is reached. In other cases, postnatal neurogenesis continues as constitutive neurogenesis into adulthood leading to a net increase of the number of neurons with age. Yet, in other cases, stem cells fuel neuronal turnover. An example is protracted development of the cerebellar granular layer in mammals and birds, where neurogenesis continues for a few weeks postnatally until the granular layer has reached its definitive size and stem cells are used up. Cerebellar growth also provides an example of continued neurogenesis during adulthood in teleosts. Again, it is the granular layer that grows as neurogenesis continues and no definite adult cerebellar size is reached. Neuronal turnover is most clearly seen in the telencephalon of male canaries, where projection neurons are replaced in nucleus high vocal centre each year before the start of a new mating season--circuitry reconstruction to achieve changes of the song repertoire in these birds? In this review, we describe these and other examples of adult neurogenesis in different vertebrate taxa. We also compare the structure of the stem cell niches to find common themes in their organization despite different functions adult neurogenesis serves in different species. Finally, we report on regeneration of the zebrafish telencephalon after injury to highlight similarities and differences of constitutive neurogenesis and neuronal regeneration.