Emission standards looking for real driving emissions assessment are demanding an update on modelling tools for combined accurate engine and aftertreatment performance evaluation, understanding these complex systems as a single element. Virtual engine models must retain accuracy while reducing computational effort to get closer to real-time computation, thus making them useful for pre-design and calibration but also potentially applicable to on-board diagnosis. This paper responds to these requirements presenting a lumped approach for aftertreament systems modelling. Fundamental operation principles of flow-through and wall-flow monoliths are covered leading the focus to the prediction of gaseous emissions conversion efficiency and particulate matter abatement. The model concept is completed with the solution of heat transfer and pressure drop processes. The lumped approach hypotheses and the solution of the governing equations for every sub-model are detailed. Heat transfer is solved applying a nodal based sub-model that accounts for gas to wall heat exchange, environment heat losses as well as monolith and external canning thermal inertia. While inertial pressure drop contributions are computed by means of the characteristic pressure drop coefficient, porous medium dynamics in wall-flow monoliths is considered separately. Thus, porous media properties conditioning pressure drop and filtration as a function of soot loading are predicted applying the spherical packed bed theory. A soot oxidation mechanism including adsorption reagent phase is presented. Concerning gaseous emissions, the general scheme to solve chemical species transport in the bulk gas and washcoat regions is described. In particular, CO and HC abatement is modelled in a close-coupled DOC-DPF brick. Model calibration procedure against a set of steady-state in-engine experiments is discussed together with a complementary computational effort evaluation to demonstrate the potential for real-time applications. As a final step, the model performance is assessed under highly dynamic driving conditions during which all modelled processes take place simultaneously.