A review of the state-of-the-art in hypersonic aeroelasticity and aerothermoelasticity is provided. Recently, the main focus in this area has been on the development of computational aeroelastic and aerothermoelastic methods capable of studying complete hypersonic vehicles. Thus, in addition to a survey of studies conducted in this area over the past six decades, two important issues are a focus of this review, namely: 1) modeling unsteady hypersonic aerodynamics; and 2) incorporation of the heat transfer between the fluid and the structure into the aeroelastic solution process. Finally, future directions of hypersonic aeroelasticity and aerothermoelasticity are outlined. Since air-breathing hypersonic vehicles exhibit strong coupling between the airframe, propulsion, and control systems, future directions point to the incorporation of advanced computational aerothermoelastic methods into a comprehensive vehicle analysis.