Adult neurogenesis can only be observed in some specific brain regions. One of these areas is the dentate gyrus of the hippocampal formation. The progenitor cells located in the subgranular layer of the dentate gyrus proliferate, differentiate, and give rise to young neurons that can become integrated into existing neuronal circuits. Under physiological conditions, hippocampal neurogenesis is linked to hippocampal-dependent learning, whereas deficits in adult hippocampal neurogenesis have been shown to correlate with disturbances in spatial learning and memory. This review summarizes the phenomenon of adult hippocampal neurogenesis and the use of suitable markers for the investigation of adult hippocampal neurogenesis. In addition, we focused on the disturbances in neurogenesis that can be seen in depression. Interestingly, several antidepressants have been found to be capable of increasing the rate of hippocampal neurogenesis. Based on that, it can be speculated that factors, which directly or indirectly increase the rate of hippocampal neurogenesis, may be helpful in the treatment of depression.