The aerodynamic analysis of wings and their vortex wakes is discussed from a perspective of its relation to the 1938 work of Ka´rma´n and Sears. The key concepts from this early paper on the analysis of airfoils in small amplitude unsteady motion are reviewed. These concepts are then used as a point of departure for developing techniques for calculating and interpreting the aerodynamic characteristics of both airfoils in large amplitude motion with deforming vortex wakes, and maneuvering low-aspect-ratio wings with leading-edge separation. Calculated examples are presented for this extended set of applications, and are compared to related analyses and experiments.