The general rules adopted in the development of automotive emission control catalytic converter models are to quantify all the essential physical and chemical phenomena related to the converter performance by separate laboratory experiments, and to minimize the complexity of the models by excluding from the models the less important phenomena. By adhering to these rules, predictive catalytic converter math models were constructed for both particle or monolithic support catalysts using either noble or base metal as active ingredients. The models have been used as a useful research and development tool for exploring the direction for improving total emission control systems, including catalyst development, engine calibration modification, converter location and converter design studies. The strategy in the application of the models is to maintain a continuous dialogue between test results and the math model predictions to a total vehicle-converter system that can meet stated goals. The power of the models is demonstrated by several practical examples, including identification of catalyst and engine modification required to meet U.S. 1976 emission standards, use of math models to focus on specific vehicle developments, and assist in the interpretation of emission control system test data.