It is widely acknowledged that neural stem cells generate new neurons through the process of neurogenesis in the adult brain. In mammals, adult neurogenesis occurs in two areas of the CNS: the subventricular zone and the subgranular zone of the dentate gyrus of the hippocampus. The newly generated cells display neuronal morphology, generate action potentials and receive functional synaptic inputs, their properties being equivalent to those of mature neurons. Alzheimer’s disease (AD) is the widespread cause of dementia, and is an age-related, progressive and irreversible neurodegenerative disease that results in massive neuronal death and deterioration of cognitive functions. Here, we overview the relations between adult neurogenesis and AD, and try to analyse the controversies in the field. We also summarise recent data obtained in the triple transgenic model of AD that show time- and region-specific impairment of neurogenesis, which may account for the early changes in synaptic plasticity and cognitive impairments that develop prior to gross neurodegenerative alterations and that could underlie new rescue therapies.