Abstract: The flamelet model and flamelet/progress variable model are those turbulent combustion models originally established for low-speed flows. Studies on the extensions of the flamlelet models to supersonic compressible flows are reviewed. For the flamelet model, the assumptions of constant pressure and linear relation of static enthalpy and mixture fraction in the establishment of flamelet library are not suitable in supersonic flows. Numerical experiments reveal that: the main species concentrations in the flamelet library are not sensitive to the given pressure value, while the intermediate species concentration vary obviously with the change of the pressure; the deviation from the linear relation between static enthalpy and mixture fraction result in little influence on the obtained mean temperature field by the flamelet model. For the flamelet/progress variable model, the chemical source terms stored in the library are found very sensitive to the flow compressibility effects. The current compressibility corrections for this problem are designed based on a rescaling to the mean source terms after PDF integration using the library not considering compressibility effects. Numerical results indicate that the compressible rescaling method reasonably incorporates the influences of the high-Mach-number effects on the tabulated source term of the progress variable and effectively improves the simulation accuracy of the flamelet/progress variable model for supersonic combustion flows.