Aerobic glycolysis is a form of glucose-inefficient metabolism that occurs when cells metabolize glucose without oxygen, despite oxygen being abundant. Aerobic glycolysis occurs in the brain, and presents a metabolic paradox: this inefficient metabolic process is a hallmark consequence of neural activity, yet, all else being equal, evolution should favor energy-efficiency. We review this paradox and propose a solution, formalized as the efficiency tradeoff hypothesis: aerobic glycolysis, despite its glucose-inefficiency, allows for information-efficient communication. Aerobic glycolysis allows for both thin, information-efficiency axons, and a tight coupling between energy production and unpredictable, rapid-on/rapid-off energy demands. We review the surrounding empirical context, finding convergent evidence and support for a novel interpretation of the blood-oxygen level-dependent (BOLD) signal. We hypothesize that the BOLD signal, which is closely related to aerobic glycolysis, indexes bottom-up sensory encoding, or more specifically, prediction error in predictive processing models. Finally, we elaborate on the implications of our review for the roles of metabolism in (a) the evolution of human cytoarchitecture, (b) social behavior, and (c) mental illness.