This paper presents different strategies for Diesel Oxidation Catalyst(DOC)modeling. Starting from the commonly used approach of describing the chemical and energy balances by first principles and fitting a small set of parameters often unknown, special emphasis is placed on data driven DOC modeling. Considering black as well as grey box approaches it is shown that the data driven methods provide a better model quality and, in the specific case, are easier to fit since the considered model class are polynomial NARX models, which are linear in parameters.