The fundamental premise that energy demands constrain neural computation has led to the widely held belief that cognitive activity is always metabolically costly. However, brain imaging and whole-body measurements in mammals demonstrate that solving cognitive tasks is typically accompanied by either a minimal increase of overall energy expenditure or no change at all. In this article, we review the relevant experimental evidence and describe why maintaining the resting state can be as costly as engaging in explicit tasks. Refraining from cognitive activity might often not be an efficient way to save energy, which has important implications for understanding the metabolic bases of brain function and behavior. For example, the pervasiveness of non-instrumental activity (such as curiosity-driven information seeking) can be readily explained from an evolutionary angle if reducing exploration does not result in significant decrease of metabolic costs. We propose that addressing the question of how different homeostatic mechanisms interact to keep the overall brain energy expenditure relatively steady will help to uncover the fundamental principles of neural computation.