Great efforts have been made over the last few decades in understanding of the mechanisms and phenomenology of soot formation and buout in combustion systems.In this paper,theoretical advances in modelling soot formation and oxidation under engine circumstance are surveyed based on the published works,particularly focus on the practical soot modelling coupled with engine computational fluid dynamics (CFD) numerical studies.The types of soot models can be divided up into three main groups: empirical,semi-empirical and detailed soot model.With the development of computing technology and increasingly comprehensive soot fundamental knowledge,the semi-empirical phenomenological soot model with major generic processes of soot formation was proposed,which is one of the most extensively investigated soot models in recent years.It is highlighted with solving mathematical equations to get soot particle number density,soot volume and mass fraction.When coupled with fuel chemistry,the detailed soot model seeks to predict soot characteristics based on molecule structure,bringing further insight of the soot evolution and transient behavior of soot-relevant species.Therefore,the sooting tendency from engine combustion fueled with alteative and oxygenated fuels are able to be further explored,which is conductive to propose new engine technologies for soot mitigation and future fuel strategy.