In fishes and salamanders, but not mammals, neural stem cells switch back to neurogenesis after injury. The signalling environment of neural stem cells is strongly altered by the presence of damaged cells and an influx of immune, as well as other, cells. Here, we summarise our recently expanded knowledge of developmental, physiological and immune signals that act on neural stem cells in the zebrafish central nervous system to directly, or indirectly, influence their neurogenic state. These signals act on several intracellular pathways, which leads to changes in chromatin accessibility and gene expression, ultimately resulting in regenerative neurogenesis. Translational approaches in non-regenerating mammals indicate that central nervous system stem cells can be reprogrammed for neurogenesis. Understanding signalling mechanisms in naturally regenerating species show the path to experimentally promoting neurogenesis in mammals.