Conventional Oxidation Catalysts are widely used in Diesel engines for their capability to achieve a huge reduction of CO and HC and, at the same time, to improve SCR catalysts performance promoting NO conversion into NO2 and generating exotherm. However, when the catalyst temperature is below the light-off, as it happens during a cold-start phase, the conversion performances are inadequate. This issue is further complicated by the upcoming regulations on CO2 that, due to the required improvements on combustion efficiency and heat loss reduction, will cause gas temperature at engine-out to decrease. Furthermore, the heating of the Exhaust Aftertreatment System by fuel-based strategies should necessarily be limited to contain the fuel penalty. In this context, the Electrically Heated Catalyst (EHC) is a solution to quickly warm up the exhaust line and reduce CO2 penalties. The increasing complexity and the need to account for competing performances require the physical based numerical simulation to reduce time and cost of the entire Exhaust Aftertreatment System development process, from the hardware design to software calibration. This paper focuses on the physical based model development for both conventional and electrically heated DOC (eDOC). GT-SUITE® was selected as simulation environment. The main steps of the applied methodology are described, including the lab-scale characterization, the definition and calibration of the kinetic scheme and the setup of the substrate parameters set. Finally, the comparison between simulation results and experimental data is presented in driving cycle conditions, showing a good capability of the models in capturing the main features of the system behavior and proving then their suitability in supporting the various steps of the overall development process.