Aeroelastic flutter is a dynamically complex phenomenon that has adverse and unstable effects on elastic structures. It is crucial to better predict the phenomenon of flutter within the scope of aircraft structures to improve upon the design of their wings. This review aims to establish fundamental guidelines for flutter analysis across subsonic, transonic, supersonic, and hypersonic flow regimes providing a thorough overview of established analytic, numerical, and reduced-order models as applicable to each flow regime. The review will shed light on the limitations and missing components within the previous literature on these flow regimes by highlighting the challenges involved in simulating flutter. Additionally, popular methods that employ the aforementioned analyses for optimizing wing structures under the effects of flutter, a subject currently garnering significant research attention, are also discussed. Our discussion offers new perspectives that encourages collaborative effort in the area of computational methods for flutter prediction and optimization.