Adenosine, acting both through G-protein coupled adenosine receptors and intracellularly, plays a complex role in multiple physiological and pathophysiological processes by modulating neuronal plasticity, astrocytic activity, learning and memory, motor function, feeding, control of sleep and aging. Adenosine is involved in stroke, epilepsy and neurodegenerative pathologies. Extracellular concentration of adenosine in the brain is tightly regulated. Adenosine may be generated intracellularly in the central nervous system from degradation of AMP or from the hydrolysis of S-adenosyl homocysteine, and then exit via bi-directional nucleoside transporters, or extracellularly by the metabolism of released nucleotides. Inactivation of extracellular adenosine occurs by transport into neurons or neighboring cells, followed by either phosphorylation to AMP by adenosine kinase or deamination to inosine by adenosine deaminase. Modulation of the nucleoside transporters or of the enzymatic activities involved in the metabolism of adenosine, by affecting the levels of this nucleoside and the activity of adenosine receptors, could have a role in the onset or the development of central nervous system disorders, and can also be target of drugs for their treatment. In this review, we focus on the contribution of 5′-nucleotidases, adenosine kinase, adenosine deaminase, AMP deaminase, AMP-activated protein kinase and nucleoside transporters in epilepsy, cognition, and neurodegenerative diseases with a particular attention on amyotrophic lateral sclerosis and Huntington’s disease. We include several examples of the involvement of components of the adenosine metabolism in learning and of the possible use of modulators of enzymes involved in adenosine metabolism or nucleoside transporters in the amelioration of cognition deficits.