Air intake plays the primary role of providing air required for the combustion process to the combustor and is responsible for engine efficiency. So having efficient air intake is one of the main concerns when it comes to designing of an aircraft propulsion system. An air intake faces several challenges, especially at supersonic and hypersonic regimes. Shockwaves are formed at these regimes. So, air intake must be designed in such a way that it manages these shockwaves efficiently. Several problems, like shockwave-boundary layer interaction, inlet buzz, unstart condition, lead to degrade the performance of the air intake, such as pressure recovery, flow distortion, etc. This study focuses on discussing these challenges associated with the supersonic air intake and also sheds light on the methods and solutions offered by different researchers to tackle these problems. Through comparative approach the most efficient solutions have also been provided in this study to help with future research and findings.