Mathematical models of fatigue and performance are potentially powerful tools to predict the effects of duty-rest schedules in many situations. Most current models, including the Circadian Alertness Simulator (CAS), derive from the two-process theory of sleep regulation. In these models, performance and fatigue are determined by a homeostatic process that depends solely on sleep/wake history, and a circadian process, driven by the biological clock. These models assume: 1) performance capability recovers in an exponential manner during sleep; 2) the homeostatic and circadian processes are additive. Current evidence suggests that both assumptions require modification. An attractive feature of the CAS is that it computes alertness curves for individuals, based on individual sleep/wake histories and other data. However, statistical evaluation is usually based on group data, with few performance metrics. As in other models, there is no substantive theory to connect the alertness computation with specific cognitive or psychomotor functions.