The continuous drive for increased fuel efficiency and sustained innovation in the automobile industry requires the adoption of radically new technological advances. Road vehicle aerodynamic design is primarily concerned with reduction in the drag and generation of a downforce. Current trends in both aircraft and wind turbine blade design show significant interest in shape-adaptive (morphing) advanced structural concepts for improved aerodynamic performance or the realization of new functionality. Morphing structures are also of interest because they have the potential to create designs of simple construction and reduced mass. However, there is an inherent contradiction between the need to create compliant structures to keep actuator demands low and the requirement for designing stiff load-carrying structures. This highlights the key design challenge for morphing structures. Ways of addressing these conflicting demands include the use of advanced composite materials which have extremely anisotropic stiffness properties or multistable behaviour. This review provides a perspective on recent developments in research on morphing structures and the potential applications for these emerging technologies in automobile aerodynamic design.