Neural stem cells (NSC) have been implicated not only in brain development and neurogenesis but also in tumourigenesis. Brain tumour stem cells (BTSC) have been isolated from several paediatric or adult human brain tumours, however their origin is still disputed. This review discusses the normal role of NSC in the adult mammalian brain and their anatomical location. It compares the molecular characteristics and the biological behaviour of NSC/BTSC, and describes the molecular pathways involved in controlling self-renewal and maintenance of adult NSC/BTSC and brain tumour development. It also assesses the current hypotheses about the origin of BTSC and the clinical consequences.