Establishing the existence and extent of neurogenesis in the adult brain throughout the animals including humans, would transform our understanding of how the brain works, and how to tackle brain damage and disease. Obtaining convincing, indisputable experimental evidence has generally been challenging. Here, we revise the state of this question in the fruit-fly Drosophila. The developmental neuroblasts that make the central nervous system and brain are eliminated, either through apoptosis or cell cycle exit, before the adult fly ecloses. Despite this, there is growing evidence that cell proliferation can take place in the adult brain. This occurs preferentially at, but not restricted to, a critical period. Adult proliferating cells can give rise to both glial cells and neurons. Neuronal activity, injury and genetic manipulation in the adult can increase the incidence of both gliogenesis and neurogenesis, and cell number. Most likely, adult glio- and neuro-genesis promote structural brain plasticity and homeostasis. However, a definitive visualisation of mitosis in the adult brain is still lacking, and the elusive adult progenitor cells are yet to be identified. Resolving these voids is important for the fundamental understanding of any brain. Given its powerful genetics, Drosophila can expedite discovery into mammalian adult neurogenesis in the healthy and diseased brain.