Diesel Particulate Filters (DPFs) are regarded as the most effective technology to reduce particulate matter (PM) emissions from modern diesel engines. PM mass collected inside the filter needs to be periodically oxidized to clean the porous walls in order to avoid excessive backpressure that could negatively affect engine and turbocharger performances leading to higher fuel consumption. Diesel Oxidation Catalysts (DOCs), on the other hand, represent an effective means to reduce hydrocarbon (HC) emissions and set the proper chemical conditions at the inlet of the DPF to enhance soot oxidation during filter regeneration. Due to the impact that these devices have on tailpipe emissions, monitoring functions aimed at assessing the health of these systems need to be implemented in the engine on-board diagnostics (OBD) system. Further, in-depth understanding of filtration and regeneration mechanisms, together with the ability of predicting actual DPF loading conditions, could play a key role in optimizing regeneration strategies adopted to keep the particulate filter within safe operating conditions. Hence, the use of real-time, yet accurate models is of primary importance to face with advanced control challenges, such as the integration of DOCs and DPFs with the engine or other critical aftertreatment components, or to properly develop model-based OBD monitors. This study aims at addressing the challenges related with real-time modeling of both DOCs and DPFs with special regard to the calibration of key parameters. At first, the development of a 1-D model for the diesel oxidation catalyst is presented;: two different approaches representing two different trade-offs in terms of model complexity/speed are discussed and analyzed. A 1-D model of a DPF is then presented, addressing the coupling of filtration and regeneration over cake, washcoat and wall thicknesses. Moreover, the approach followed to develop the DPF model is innovative as it is directly integrated via analytical functions, thus improving the discretized approach used in similar models. Finally, an innovative model tuning methodology called Virtual Conditioning is presented and applied to generate robust model calibrations. Numerical results are compared with experimental data gathered at West Virginia University's (WVU) Engine and Emissions Research Laboratory (EERL) using a Mack heavy-duty diesel engine coupled to a Johnson Matthey C-CRT aftertreatment system. The study shows that: a) DOC model is capable of replicating measured outlet emissions concentrations with an accuracy of 15% and minimal computational requirements over both steady-state and transient operating conditions; b) DPF wall and washcoat layer present different regeneration and collection dynamics, whose behavior is important to capture filter pressure drop and temporal evolution of the collected mass; c) advanced filtration and regeneration process treatment in the wall together with a robust calibration process allow for the use of constant model parameters to replicate combinations of ...