For high-intensity muscular exercise, the time-to-exhaustion (t) increases as a predictable and hyperbolic function of decreasing power (P) or velocity (V). This relationship is highly conserved across diverse species and different modes of exercise and is well described by two parameters: the 'critical power' (CP or CV), which is the asymptote for power or velocity, and the curvature constant (W') of the relationship such that t = W'/(P-CP). CP represents the highest rate of energy transduction (oxidative ATP production, V? O2) that can be sustained without continuously drawing on the energy store W' (composed in part of anaerobic energy sources and expressed in kilojoules). The limit of tolerance (time t) occurs when W' is depleted. The CP concept constitutes a practical framework in which to explore mechanisms of fatigue and help resolve crucial questions regarding the plasticity of exercise performance and muscular systems physiology. This brief review presents the practical and theoretical foundations for the CP concept, explores rigorous alternative mathematical approaches, and highlights exciting new evidence regarding its mechanistic bases and its broad applicability to human athletic performance.