The after-treatment of exhaust gas using 3-way catalytic converters is now normal practice in automotive applications. For other applications, such as outboards, motorcycles and utility engines, new legislation is now in place in both Europe and North America. Further reduction of the permitted emission levels require the use of catalysts for two-stroke engine applications. However, current automotive catalyst systems are not suitable for durable operation in most two-stroke engines and new analytical tools are required to aid the development engineers in the implementation of revised designs and operating strategies.This paper reviews the range of modeling techniques which have been developed for automotive uses and presents new and modified models suitable for two-stroke engines. This requires particular emphasis to be placed on the oxidation reactions that predominate in the two-stroke engine exhaust. Several types of model are reviewed, using both phenomenological and theoretical methods. The applicability and accuracy of each model is considered and compared with experimental results. In each case, the thermodynamic and gas dynamic aspects and the limitations of the models are explained.Finally, the future direction of modeling is outlined, in the light of current requirements and some recommendations are made for the evolution of a catalyst simulation suitable for use within a full engine model.