In this videotaped lecture, Cathleen S. Morawetz brings a wealth of distinguished research experience to bear on recent developments in the area of transonic flow and the associated differential equations. The talk begins with a short review of mixed equations (for many cases, including transonic flight, flow is governed partly by elliptic and partly by hyperbolic equations) and moves on to a discussion of compressible flow. (Phoenix, AZ, 1989)