The advent of stricter U.S. and European exhaust emissions regulations has increased the need for reliable 3-way catalytic converter models supporting the design of demanding exhaust systems for low-emitting vehicles. Although a number of tunable models have been presented in the literature, their efficient performance in actual 3-way applicaions requires further development and validation. The major difficulties posed in such modeling efforts arise from the complexities in the reaction schemes and the respective rate expressions for the multitude of currently used catalyst formulations. This paper addresses the details of tuning and real world application of a two-dimensional catalytic converter model, which accounts for the HC (hydrocarbons) and CO oxidation, as well as NO reduction reactions. The model features a number of innovations regarding the catalyst transient behaviour modelling and the reaction kinetics scheme. The advanced oxygen storage submodel presented is capable of accounting for the redox and temperature dependence of the oxygen availability under transient operation. The redox sensitivity of the reaction scheme allows to get clearer insight in the "lambda-window" behavior of 3-way catalysts. It is concluded, that mathematical modelling may successfully describe important aspects of real world three-way catalytic converter operation under dynamic conditions, and thus, is a valid tool in exhaust aftertreatment systems optimization.