The basis of the scientific method is the development of intellectual models, the predictions of which are then subjected to scientific evaluation. The more robust test of any such model is one that aims to refute or falsify its predictions. Successful refutation forces revision of the model: the revised model persists as the "truth" until its predictions are, in turn, refuted. Thus, any scientific model should persist only as long as it resists refutation. An unusual feature of the exercise sciences is that certain core beliefs are based on an historical physiological model that, it will be argued, has somehow escaped modern, disinterested intellectual scrutiny. This particular model holds that the cardiovascular system has a limited capacity to supply oxygen to the active muscles, especially during maximal exercise. As a result, skeletal muscle oxygen demand outstrips supply causing the development of skeletal muscle hypoxia or even anaerobiosis during vigorous exercise. This hypoxia stimulates the onset of lactate production at the "anaerobic," "lactate," or ventilation thresholds and initiates biochemical processes that terminate maximal exercise. The model further predicts that the important effect of training is to increase oxygen delivery to and oxygen utilization by the active muscles during exercise. Thus, adaptations that reduce skeletal muscle anaerobiosis during exercise explain all the physiological, biochemical, and functional changes that develop with training. The historical basis for this model is the original research of Nobel Laureate A. V. Hill which was interpreted as evidence that oxygen consumption "plateaus" during progressive exercise to exhaustion, indicating the development of skeletal muscle anaerobiosis. This review confirms that Hill's research failed to establish the existence of the "plateau phenomenon" during exercise and argues that this core component of the historical model remains unproven. Furthermore, definitive evidence that skeletal muscle anaerobiosis develops during submaximal exercise at the anaerobic threshold initiating lactate production by muscle and its accumulation in blood is not currently available. The finding that exercise performance can improve and metabolism alter before there are measurable skeletal muscle mitochondrial adaptations could indicate that variables unrelated to oxygen use by muscle might explain some, if not all, training-induced changes. To accommodate these uncertainties, an alternate physiological model is proposed in which skeletal muscle contractile activity is regulated by a series of central, predominantly neural, and peripheral, predominantly chemical, regulators that act to prevent the development of organ damage or even death during exercise in both health and disease and under demanding environmental conditions. During maximal exercise, the peripheral regulation of skeletal muscle function and hence of oxygen use by skeletal muscle, perhaps by variables related to blood flow, would prevent the development of muscle rigor, especially in persons with an impaired capacity to produce ATP by mitochondrial or glycolytic pathways. Regulation of skeletal muscle contractile function by central mechanisms would prevent the development of hypotension and myocardial ischemia during exercise in persons with heart failure, of hyperthermia during exercise in the heat, and of cerebral hypoxia during exercise at extreme altitude. The challenge for future generations of exercise physiologists is to identify how the body anticipates the possibility of organ damage and evokes the appropriate control mechanism(s) at the appropriate instant.