1988 by the American Institute of Aeronautics and Astronautics, Inc. We discuss mostly the theoretical aspects of our approach to inverse airfoil design. The methods we propose to solve the inverse airfoil problem for subcritical and supercritical flows are based on the formulation of the problem in the potential plane. Some of our methods have been used to generate subcritical airfoils. Further numerical work for subsonic and transonic cases is in progress.