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Supersonic and hypersonic flows have gained considerable attention in the aerospace industry in recent years. Flow control is crucial for refining the quality of these high-speed flows and improving the performance and safety of fast aircraft. This paper discusses the distinctive characteristics of supersonic flows compared to low-speed flows, including phenomena such as boundary layer transition, shock waves, and sonic boom. These traits give rise to significant challenges related to drag, noise, and heat. Therefore, a review of several active and passive control strategies is provided, highlighting their significant advancements in flow transitions, reducing drag, minimizing noise, and managing heat. Furthermore, we provide a comprehensive analysis of various research methodologies used in the application of flow control engineering, including wind tunnel testing, flight testing, and computational fluid dynamics (CFD). This work gives an overview of the present state of flow control research and offers insights into potential future advancements.