The current study presents the modelling of turbulent non-premixed or premixed flames over a range of combustion regimes using a variety of fuel mixtures. A parabolic Finite Volume method is used for the flow solution coupled to a joint-scalar transported Probability Density Function (PDF) approach for the inclusion of the thermochemistry without approximation. Finite chemistry effects were studied for two different cases. Moderate or Intense Low Oxygen Dilution (MILD) combustion is quantified with excellent pollutant formation, showing a reduction in temperature gradients and an increasing distributed reaction zone with dilution. High shear flows with low Damköhler numbers are also investigated with the appearance of a neck zone and distributed reaction at higher jet velocities. Transported PDF methods produce good agreement with experimental results, where discrepancies in the mixing model and flow field characterisation are apparent. Molecular mixing is closed using the modified Curl's model which provides reasonable mixing behaviour. Further studies into improvements upon the micro-mixing model are encouraged. Additionally, sensitivity to boundary conditions is demonstrated. The cases studied contribute to the understanding of emerging trends in practical combustion devices and portray finite-chemistry effects such as extinction and re-ignition.