Animals that fly must be able to do so over a huge range of aerodynamic conditions, determined by weather, wind speed and the nature of their environment. No single parameter can be used to determine-let alone measure-optimum flight performance as it relates to wing shape. Reconstructing the wings of the extinct pterosaurs has therefore proved especially problematic: these Mesozoic flying reptiles had a soft-tissue membranous flight surface that is rarely preserved in the fossil record. Here, we review basic mechanical and aerodynamic constraints that influenced the wing shape of pterosaurs, and, building on this, present a series of theoretical modelling results. These results allow us to predict the most likely wing shapes that could have been employed by these ancient reptiles, and further show that a combination of anterior sweep and a reflexed proximal wing section provides an aerodynamically balanced and efficient theoretical pterosaur wing shape, with clear benefits for their flight stability.