This paper is concerned with a discussion of some of the problems of flutter and aeroelasticity that are or may be important at high speeds. Various theoretical procedures for treating high Mach number flutter are reviewed. Application of two of these methods, namely, the Van Dyke method and piston-theory method, is made to a specific example and compared with linear two- and three-dimensional results. It is shown that the effects of thickness and airfoil shape are destabilizing as compared with linear theory at high Mach number. In order to demonstrate the validity of these large predicted effects, experimental flutter results are shown for two rectangular wings at Mach numbers of 6.86 and 3. The results of nonlinear piston-theory calculations were in good agreement with experiment, whereas the results of using two- and three-dimensional linear theory were not. In addition, some results demonstrating the importance of including camber modes in a flutter analysis are shown, as well as a discussion of one case of flutter due to aerodynamic heating.