An overview is provided of computational methods that can be used in solving the design problem of aerodynamics; i.e. the problem of finding the detailed shape of (parts of) configurations of which the gross geometric characteristics have already been determined in a preliminary, overall design process, and that, subject to certain constraints, have to meet given aerodynamic requirements. Attention is focussed on methods for solving the classical inverse problem of aerodynamics and on approaches using optimization techniques. Both methods limited to subsonic flow utilizing panel method technology as well as methods based on finite difference/volume formulations for compressible, transonic flow are covered. In conclusion a discussion is presented of the relative merits of the various computational approaches to the problem of aerodynamic design