The classical trade off between nitrogen oxides (NO x) and particulate matters (PM) is still one of the key topics for Diesel engine developers. This article gives an overview about models for these emissions usable for online engine and exhaust after treatment control, offline optimization and virtual sensors for monitoring. Two different ways for obtaining such models are presented in detail: first we present a black-box data-based mean value model which estimates engine raw emissions from quantities available in the engine control unit. Second a gray-box model is shown in which also physical equations are used to describe emission formation over crank angle with the measured cylinder pressure as main input. © 2010 Springer-Verlag London.