We define stem cells by two hallmark characteristics: multipotentiality and self-renewal. In this thesis, we investigate the role of Notch---a conserved intercellular signalling pathway---in neural stem cell (NSC) behaviour. We provide evidence that Notch signalling is essential for the maintenance of the NSC population. In embryos, Notch signalling is required for all NSCs to undergo expansionary symmetric divisions (ESD), regardless of the cellular environment. Within the adult, however, Notch signalling modulates the cell cycle time in order to prevent brain NSC exhaustion. Thus, Notch signalling effects in the embryo and adult appear different. Hypotheses are discussed which attempt to resolve this discrepancy, including the ability of the cell cycle to modify the mode of division. To account for the mode of division and cell cycle modifications, a model is proposed: With increasing cell cycle time, an ESD can be converted to an asymmetric and then finally, to a terminal symmetric division.