A universal constraint on the evolution of brains is that the nervous system’s computational power is limited by its energy supply. By describing an energy budget for the grey matter of the mammalian CNS, I will explain how key design features of the brain are partly determined by the energy supply the brain receives as oxygen and glucose, and how matching of brain energy supply to brain energy use underpins BOLD functional magnetic resonance imaging. I will examine why the white matter uses less energy than the grey matter, and whether myelination really saves energy. I will present a simple account of how information flow through synapses relates to the energy used by the synapses and show that this explains why synapses are unreliable transmitters of information. I will outline why the primary locus of control of the brain’s energy supply, and hence of the generation of BOLD fMRI signals, is in capillaries rather than arterioles.