Applying the computational fluid dynamics tool kit to the analysis and design of airfoil aerodynamics, this chapter explores the details of the shape-to-performance mapping under a variety of flight conditions, from low subsonic to transonic and supersonic speeds. The mappings change with the intended design goal, be it more laminar flow, higher maximum lift coefficient, or increased drag divergence speed. Through computations one sees correlations between these performance measures and shape factors such as thickness and camber distributions. One also sees clear historical progress in design methods. The earliest NACA airfoils during the 1920s were designed mainly in a cut-and-try approach. Aided by a theoretical method for predicting airfoil aerodynamics, the designs in the 1930s–1950s improved performance significantly. During the 1970s, NASA then resumed work combining a computational inverse procedure with supportive wind-tunnel measurements that produced the new technology family of NASA airfoils. This chapter investigates and compares some of them. It continues with a high-lift example analyzing the three-element slat-airfoil-flap test case L1T2 and comparing the predicted increases in lift with that measured in experiments for these high-lift devices. The final example – airfoil design by mathematical single-point optimization – reshapes the RAE2822 airfoil to minimize the wave drag at cruise conditions.