Stem cells are capable of extensive self-renewal while preserving the ability to generate cell progeny that can differentiate into different cell types. Here, we describe some methods for the isolation of neural stem cells (NSCs) from the adult murine subependymal zone (SEZ), their extensive culturing and the assessment of their full developmental potential, particularly with respect to their differentiation capacity. The procedure includes chemically defined conditions such as absence of serum and addition of specific growth factors, in which differentiated cells die and are rapidly eliminated from the culture. In contrast, undifferentiated precursors become hypertrophic and proliferate, forming clonal spherical clusters called "neurospheres." Experimental manipulation of NSCs identifies populations of cells with differential restriction in their self-renewal potential and introduces a great interest in defining the conditions that guide their differentiation into a variety of neuronal and glial subtypes, aspects that have important implications for their use in future clinical purposes.