High-speed air intakes often exhibit intricate flow patterns, with a specific type of flow instability known as `buzz’, characterized by unsteady shock oscillations at the inlet. This paper presents a comprehensive review of prior research, focused on unraveling the mechanisms that trigger buzz and its implications for engine stability and performance. The literature survey delves into studies concerning complex-shaped diffusers and isolators, offering a thorough examination of flow aerodynamics in unstable environments. Furthermore, this paper provides an overview of contemporary techniques for mitigating flow instability through both active and passive flow control methods. These techniques encompass boundary layer bleeding, the application of vortex generators, and strategies involving mass injection and energy deposition. The study concludes by discussing future prospects in the domain of engine-intake aerodynamic compatibility. This work serves as a valuable resource for researchers and engineers striving to address and understand the complexities of high-speed air induction systems.