To feed people in the coming decades, an increase in sustainable animal food production is required. The efficiency of the global food production system is dependent on the knowledge and improvement of its submodels, such as food animal production. Scientists use statistical models to interpret their data, but models are also used to understand systems and to integrate their components. However, empirical models cannot explain systems. Mechanistic models yield insight into the mechanism and provide guidance regarding the exploration of the system. This review offers an overview of models, from simple empirical to more mechanistic models. We demonstrate their applications to amino acid transport, mass balance, whole-tissue metabolism, digestion and absorption, growth curves, lactation, and nutrient excretion. These mechanistic models need to be integrated into a full model using big data from sensors, which represents a new challenge. Soon, training in quantitative and computer science skills will be required to develop, test, and maintain advanced food system models.