Some theorems are established for the slope and curvature radius of an airfoil contour obtained by conformal mapping, the velocity gradient along it, and the curvature of streamlines. Following a discussion on some general features of the conformal mapping for a wide range of airfoil shapes, the flow behavior near the trailing edge is carefully examined. It is shown that, in potential flow, the emerging streamline there has infinite curvature, except at a singular angle of attack. One infers that the interplay between the external flow and the boundary layer will produce, at each flow regime, an equivalent airfoil contour (with the displacement thickness added), having such a shape at the trailing edge that its singular angle of attack, rendering the streamline curvature finite, would coincide with the actual incidence. This might require a certain amount of separation; therefore, by suitably shaping the trailing edge of the real airfoil, e.g., with a small moving tab, one may alter the contour to avoid detachment, and thereby reduce cruise drag by a few percent. OWADAYS j solutions to airfoil flow problems are commonly found with numerical methods, which carry out manipulations of local variables in a multitude of points throughout the flowfield. It is a pity that this recourse to brute computer force has sent into oblivion the more traditional approach, which seeks, with the help of conformal mapping and complex potentials, global solutions, valid in the whole domain and correctly representing the asymptotic conditions. Judicious use of modern computing tools multiplies the power of these methods and, as we shall try to illustrate hereafter, permits us to study the fine details of the flow, while also gaining insight into some important qualitative aspects, which are obscured by the pointillist way of painting the reality. Of particular interest is the behavior of the flow near the trailing edge since it determines the circulation (and influences also the drag); this is even more important for unsteady flows. Our endeavor will be, therefore, to show how the applictioh of certain theorems on conformal mapping and potential flow throws new lights on these classical problems and suggests interesting developments.