Accurate and useful mathematical models of physical processes can be made when we understand all of the phenomena involved. This paper reviews our understanding of the fluid flow, heat transfer and thermodynamic processes occurring in engines and the status of mathematical models expressing this understanding. Thermodynamic single system rate models are found to be extremely useful in predicting power and fuel consumption performance but of limited value in predicting emission performance. Multiple-zone, nonequilibrium models are essential for predicting emissions but are limited in accuracy by computer capacity and our understanding of engine phenomena which vary rapidly both with space and time. The need for and ability of new types of instrumentation, primarily optical, to increase our understanding of engine phenomena and improve our models is discussed.