Advances in modeling soot formation and burnout in combustion systems are surveyed. The types of models are divided up into three classes : empirical, semi-empirical and detailed. Empirical models use correlations of experimental data to predict trends in soot loadings. Semi-empirical models solve rate equations that are calibrated against experimental data. Detailed models seek to predict the concentrations of all the important species in a flame, from fuel to polyaromatic hydrocarbons to soot. The three classes of models have demonstrated success in predicting soot concentrations. However, our knowledge of some of the fundamental underlying is still open to question and the success of the models has been obtained to some degree by adjustments to fit measurements.