One of the most fundamental beliefs in exercise physiology is that performance during maximum exercise of short duration is limited by the inability of the heart and lungs to provide oxygen at a rate sufficiently fast to fuel energy production by the active muscle mass. This belief originates from work undertaken in the 1920's by Hill and Lupton. A result is that most, if not all, of the studies explaining the effects of exercise training or detraining or other interventions on human physiology explain these changes in terms either of central adaptations increasing oxygen delivery to muscle or of peripheral adaptations that modify the rates of oxygen or fuel utilization by the active muscles. Yet a critical review of Hill and Lupton's results shows that they inferred but certainly did not prove that oxygen limitation develops during maximal exercise. Furthermore, more modern studies suggest that, if such an oxygen limitation does indeed occur during maximal exercise, it develops in about 50% of test subjects. Thus, an alternative mechanism may need to be evoked to explain exhaustion during maximal exercise in a rather large group of subjects. This review proposes that the factors limiting maximal exercise performance might be better explained in terms of a failure of muscle contractility ("muscle power"), which may be independent of tissue oxygen deficiency. The implications for exercise testing and the prediction of athletic performance are discussed.