Diesel engines find applications in many areas such as transportation of passengers/goods, farm machines, Generators, and construction equipment. The number of diesel-fueled engines is very large and is expected to increase further with time. However, diesel engines are responsible for anthropogenic NOx and soot emissions. To comply with the stringent future emission regulations, ways of inhibiting the formation of these emissions need to be explored further. Lowtemperature combustion (LTC) strategies such as homogeneous charge compression ignition (HCCI), reactivity controlled compression ignition (RCCI), partially premixed charge compression ignition (PCCI) have the capabilities of ultra-low NOx and Soot emission formation. These LTC strategies improve the fuel-air mixing and reduce the peak combustion temperature, leading to low NOx and Soot emissions. These combustion strategies face challenges in controlling combustion, maintaining combustion stability, and operating the engine at a high load. Engine modelling could play a role in predicting Soot and NOx emissions from these complex combustion strategies. In this chapter, an effort has been made to understand the fundamentals of soot and NO x modelling. It is essential to understand the chemical mechanisms of NOx and soot formation for accurate modelling. Empirical and phenomenological models for soot and NO x formation mechanisms, factors affecting them, Zeldovich mechanism, and prompt NOx formation mechanisms are discussed. Hiroyasu-NSC model, Waseda model, Gokul model, and Dalian model to understand the soot formation and their capabilities are discussed in detail. The two most fundamental semiempirical models for NO x formation based on the Zeldovich mechanism and the prompt NO x (Fenimore mechanism) are also discussed.