A comprehensive selective catalytic reduction (SCR) model is developed to detail the global kinetic reactions in the catalyst which is involved in two type of sites for high- and low-temperature NH3 adsorption/desorption, as well as a low temperature H2O storage. The model accounts for the formation of ammonium nitrate in fast SCR and the decomposition formation of ammonium nitrate in the absence of NO, and addresses N2O relative to NO and NO2 reactions with NH3. The model has been validated against commercial Cu-SSZ-13 measurements of NH3 inventory, NH3 oxidation, NO oxidation, standard SCR, fast SCR and NO2 SCR at both comprehensive steady-state and transient conditions. In addition, the application of the SCR model for emissions control over a transient drive cycle at cold start was demonstrated based on diesel oxidation catalyst (DOC) and SCR aftertreatment system for a passenger car. The results show that the SCR model can provide the detailed emissions estimations for steady-state and transient conditions, can assist with understanding the impact of the SCR reaction mechanism, and can assist with the design and optimization of SCR catalysts to develop innovative technologies for co-optimization of engine fuel economy and emissions control technologies.