Under experimental conditions, tissue‐specific stem cells have been shown to give rise to cell lineages not normally found in the organ or tissue of residence. Neural stem cells from fetal brain have been shown to give rise to blood cell lines and conversely, bone marrow stromal cells have been reported to generate skeletal and cardiac muscle, oval hepatocytes, as well as glia and neuron‐like cells. This article reviews studies in which cells from postnatal bone marrow or umbilical cord blood were induced to proliferate and differentiate into glia and neurons, cellular lineages that are not their normal destiny. The review encompasses in vitro and in vivo studies with focus on experimental variables, such as the source and characterization of cells, cell‐tracking methods, and markers of neural differentiation. The existence of stem/progenitor cells with previously unappreciated proliferation and differentiation potential in postnatal bone marrow and in umbilical cord blood opens up the possibility of using stem cells found in these tissues to treat degenerative, post‐traumatic and hereditary diseases of the central nervous system. © 2002 Wiley‐Liss, Inc.