Soot formation is a complex phenomenon which requires the use of large chemical mechanisms not only to account for a detailed description of the small gas phase molecules but for the enormous variety of PAH. These expensive requirements have made its modelling elusive for the scientific community although acceptable results have been obtained in the last years (Yang et al. 2019, Rodrigues et al. 2018, Hoerlle and Pereira 2019). In order to increase the reliability of the simulations, a lot of work has to be done to improve PAH chemistry and their interaction with turbulence, soot modelling oxidation and simulation of particle size distribution. To sort out the difficulties that the soot solid phase introduces in the fluid mechanics simulations, the Method of Moments (MOM) (Mueller et al., 2009, Chong et al. 2019, Salenbauch et al. 2019) and the sectional model (Rodrigues et al. 2018, Hoerlle and Pereira 2019) have been used. Both methods have been coupled with flamelet combustion models providing stateof-the-art results (Rodrigues et al. 2018, Yang et al. 2019). Finally, another approach is the coupling of soot models with the Conditional Moment Closure (CMC) model for which promising results have also been obtained (Giusti et al. 2018).