This paper presents and evaluates physical and mathematical models for a detail characterization of non-premixed flames. Some of these models have been developed recently in the sequence of limitations and inconsistencies detected in the alternatives available. Among the most relevant is a new combustion model that considers intermediate chemical species. It is derived using an approach based in the characterization of the reactant plan and it illustrates that the chemical equilibrium assumption influences only partially the values of species concentrations. An important component of the model is a new probability density function, consistent with the experimental observation, which is used to account for the mean effects of the turbulence-chemistry interaction. The evaluation of the instantaneous values of temperature under non-adiabatic conditions was also investigated. The inconveniencies of a classical solution are highlighted and a new approach with the flexibility to adjust predictions to experimental values is introduced. The turbulence radiation interaction is examined and it is concluded that, in high soot content flames, the correlation between the emissive power of the gaseous mixture and the absorption coefficient can be neglected. The models are applied to predict the behaviour of a high swirling flame and it is concluded that the predictions are in good agreement with experiments.