Neural stem cells (NSCs) give rise to neurons during development. NSCs persist and neurogenesis continues in restricted regions of postnatal and adult brains. Adult-born neurons integrate into existing neural circuits by synaptic connections and participate in the regulation of brain function. Thus, understanding NSCs and neurogenesis may be crucial in the development of new strategies for brain repair. Here, we introduce the lineage of NSCs from embryonic to adult stages and summarize recent studies on maturation and integration of adult-born neurons. We also discuss the regulation and potential functions of adult neurogenesis in physiological and pathological conditions.