ESDU 98013 describes how winglets function and the aerodynamic principles governing their design. At subsonic speeds the aerodynamic efficiency of a wing (without winglets) is ultimately constrained by its span. Increasing the span permits decreases in trailing-vortex drag (at given lift) and increases in aerodynamic efficiency. Increases in aerodynamic efficiency may well entail increased structure weight and other disadvantages, and so the best practical design does not correspond to the highest aerodynamic efficiency. Design choices are also influenced by whether winglets are to be considered for an existing wing or for a new design. A simple procedure is presented for assessing the effects of winglets on cruise performance that takes into account wing structure weight. On this basis, it is found that for a new design winglets are unlikely to be worth considering unless ground operations restrict the aircraft span sufficiently. For an existing wing design, winglets may be worthwhile, and preferred over wing tip extensions, since less extensive wing strengthening may be needed to achieve a given increase in aerodynamic efficiency. Detailed comparison of alternative design changes is then needed. Achievable reductions in trailing-vortex drag are shown to be sensitive to the spanwise loading distribution of the unmodified wing. The simple treatment also indicates that it is probably better to utilise winglets having upper elements only, rather than winglets with both upper and lower elements, A number of points concerning the detailed design of winglets and the interactions between the wing and winglet are presented.