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In this thesis we investigate the supersonic combustion in scramjet combustors with strut and cavity flame holders through the Reynolds-Averaged Navier–Stokes (RANS) and Large Eddy Simulation (LES) strategies. Firstly, the Unsteady Flamelet/Progress Variable (UFPV) model for turbulent combustion in low-speed flows is introduced and extended to supersonic flows and a new strategy is developed to create probability density function look-up tables for the UFPV model. Secondly, the RANS modelling is employed to a strut-based scramjet combustor using the flamelet and UFPV models and the latter shows a better performance. Subsequently, the LES modelling is performed with the UFPV model and the UFPV model gives good predictions on comparing the numerical results to the experimental data. Thirdly, the LES modelling is employed to a cavity-based scramjet combustor. The results obtained indicate that the local extinction and autoignition events are very common phenomena in the supersonic flame and the UFPV model is able of predicting these events with reasonable accuracy. Further, an activation-energy-asymptotic-based Damköhler number concept is a valuable metric to identify flame weakening and extinction in supersonic flames. Together with the OH radicals, the distribution of the HO2 radicals can assist in identifying the autoignition events in the supersonic flame. Finally, analysing the flameholding mechanisms of the cavity, it is found that the cavity provides a stable ignition source to the fluid. Further, the combustion in the cavity is dominated by flame propagation. However, on the outer interface of the air and hydrogen streams, the combustion is mainly dominated by autoignition. Both autoignition and flame propagation contribute to the combustion in the mixing layer. Also the combustion in the cavity mixing layer has effects on the induction reactions in the wake of the hydrogen jet and reduces the induction time of the autoignition.