The processes of neural genesis, namely neurogenesis, astrogliogenesis, and oligodendrogenesis, that is, the formation of new neurons, astrocytes, and oligodendrocytes start with embryonic development. Of importance, it continues throughout adulthood, not only in the neurogenic niches where neural stem cells (NSCs) are present, but also from glial precursor cells in the brain parenchyma. Therefore, NSCs can be considered a potential therapeutic option in conditions of neural loss and tissue degeneration, as in neurodegenerative diseases. Specifically, stem cell therapy represents a personalized, localized, and probably fruitful alternative in patient care, and is the subject of ongoing research. Nevertheless, many mechanisms of this regenerative therapy remain elusive: if transplantation is required, not only is it necessary to successfully deliver these NSCs to the brain, but they also need to survive, proliferate, and replace the lost neural cells. In line with this, finding ways to manipulate the endogenous sources of NSCs is also very appealing. In particular, adenosine and caffeine (a nonselective antagonist of adenosine receptors), widely studied modulators of neuronal activity, have emerged as potential targets of neurogenesis and oligodendrogenesis. In this article, we review the present concepts on the role of adenosine in embryonic and postnatal neural cell genesis, together with its relevance in the context of brain regeneration.