Fins are crucial for flight stability and control, particularly at supersonic and hypersonic speeds. Shock waves, boundary layer behaviour, and flow separation are examples of complex aerodynamic phenomena that must be taken into account during the design phase since they significantly affect structural integrity and performance. This chapter covers the physics involved in the fin design for rocket systems and high-speed missiles and offers a literature analysis on the design and applications of fins in rockets and supersonic missiles, with a focus on optimizing the aerodynamic performance characteristics of fins. Fins are essential for flight stability and control because of their greater impact at high speeds, when aerodynamic forces significantly affect flight performance. This study examines the effects of various fin configurations on critical parameters like lift, drag, and overall stability. Fin placement, size, and other geometric changes are also taken into account to minimize wave drag. This article reviews the experimental and computational approaches to fin behaviour analysis. Special emphasis is made on the challenges of supersonic flight regimes, where phenomena like shock wave interactions, boundary layer effects, and flow separation come into effect. This paper summarizes earlier studies and provides useful information on the trade-offs necessary to strike a balance between structural durability and aerodynamic efficiency, serving as a guide for future advancements in missile and rocket fin design.