An aircraft exceeding the speed of sound can cover large distances in short amount of time and has several important applications. Thus, there has always been an interest in producing a Supersonic Transport (SST) Aircraft for commercial usage in recent decades. However, the problem of sonic boom restricts operations over inhabited/ land areas. This major obstacle to overland supersonic flight has been subject of governmental and private research for a long time. The research has two parts: minimum acceptable parameters of ground boom signatures for supersonic flight and reduction of Sonic Boom. The methods developed to reduce the boom are generally classified into Aircraft operations, Design, and Exotic methods. This paper reviews the significant methods proposed under each of these categories with special emphasis on design. Due to the range and complexity of methods proposed, there is no consensus amongst the scientific community about the design for an SST. The requirements of low boom design conflict with the requirements of carriage of an effective payload and basic aerodynamics. With the development of high- fidelity CFD and wave propagation programmes like PCBoom, analysing new designs has become easier and understanding of the contribution of various configurations on ground signatures has improved. This has led to promising developments like the X-59 research aircraft, making this field of study one of the most exciting in the aviation industry today.