Mathematical modeling is a powerful tool for understanding how sleep and caffeine consumption influence cognitive performance. This review integrates recent advancements in mathematical modeling, focusing on the Unified Model of Performance (UMP) and similar frameworks. We emphasize the significance of these models in predicting and optimizing cognitive outcomes under various conditions. Experimental data from three scenarios—moderate sleep deprivation with low caffeine, severe sleep deprivation with high caffeine, and extended sleep with moderate caffeine—demonstrate the practical applications of these models. Although the models are useful, they often overlook crucial internal and external variables. This review highlights the need for incorporating these factors into advanced models to improve performance optimization strategies.