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The probability density function approach can accurately close the turbulent/chemical reaction interaction, and has been widely used in the numerical simulation of turbulent combustion. With the continuous development of the hypersonic propulsion technology, supersonic turbulent combustion in scramjet has brought new challenges to the application of probability density function approach. At first, this paper reviews the latest progress of the application of probability density function approach to supersonic turbulent combustion. The basic theory, key models and solution framework of probability density function approach are summarized. The specific challenges and related research work of the theory, model and numerical solution of the probability density function approach for supersonic turbulent combustion are introduced, including the compressibility effect, high-speed source term model correction, and small-scale hybrid model improvement. Then, the application of probability density function approach in supersonic turbulent combustion is reviewed. Finally, the application prospects and development direction of the probability density function approach in supersonic combustion are discussed.