In 1923, Nobel Laureate A.V. Hill proposed that maximal exercise performance is limited by the development of anaerobiosis in the exercising skeletal muscles. Variants of this theory have dominated teaching in the exercise sciences ever since, but 90 years later there is little biological evidence to support Hill's belief, and much that disproves it. The cardinal weakness of the Hill model is that it allows no role for the brain in the regulation of exercise performance. As a result, it is unable to explain at least 6 common phenomena, including (i) differential pacing strategies for different exercise durations; (ii) the end spurt; (iii) the presence of fatigue even though homeostasis is maintained; (iv) fewer than 100% of the muscle fibers have been recruited in the exercising limbs; (v) the evidence that a range of interventions that act exclusively on the brain can modify exercise performance; and (vi) the finding that the rating of perceived exertion is a function of the relative exercise duration rather than the exercise intensity. Here I argue that the central governor model (CGM) is better able to explain these phenomena. In the CGM, exercise is seen as a behaviour that is regulated by complex systems in the central nervous system specifically to ensure that exercise terminates before there is a catastrophic biological failure. The complexity of this regulation cannot be appreciated if the body is studied as a collection of disconnected components, as is the usual approach in the modern exercise sciences.