This chapter provides a review, synthesis, and analysis of the literature on stimulant medications and cognitive performance. The International Civil Aviation Organization (ICAO) Fatigue Risk Management Systems Task Force (FRMS TF) describes fatigue as being associated with performance declines including decreased vigilance, increasingly variable but overall slower reaction times, forgetfulness, mood swings, and finally frank sleep onset. A number of biomathematical models have been developed to predict alertness and cognitive performance based on sleep/wake history and time of day. The Walter Reed Army Institute of Research Sleep Performance Model (WRSPM) sleep function mathematically describes recovery or restoration of performance during sleep. The circadian modulation function mathematically describes the well-characterized, cyclic daily variation in cognitive performance. This performance variation closely resembles the circadian rhythm in body temperature with a time lag of approximately 2 hours. The WRSPM wakefulness function describes the progressive decrement in performance that occurs during waking.