In the early era of aviation, Frederick Lanchester was both an inventor and a theoretician driven by the need for a theory of flight that would reduce the guesswork in designing new aircraft. His book Aerodynamics in 1907 laid down the early foundations of such a theory. The theory with contributions from others, notably Ludwig Prandtl, was refined to become the basis for the sleek designs of WWII aircraft brought about with little guesswork. New technology changed aircraft design radically with the increased speed of jet propulsion reaching into the transonic range with nonlinear aerodynamics. In the late 1940s and early 1950s substantial guesswork returned to aircraft design. The legacy of Lanchester et al., however, lived on with the development of computational fluid dynamics (CFD) that could guide designers through nonlinear transonic effects. This article presents a historical sketch of how CFD developed, illustrated with examples explaining some of the difficulties overcome in the design of the first-generation swept-wing transonic fighters. The historical study is forensic CFD in search for the likely explanation of the designer’s choice for the wing shape that went into production a long time ago. The capability of current CFD applied to the aerodynamics of aircraft with slender wings is surveyed. The cases discussed involve flow patterns with coherent vortices over hybrid wings and wings of moderate sweep. Vortex-flow aerodynamics pertains to understanding the interaction of concentrated vortices with aircraft components. Modern Reynolds-Averaged Navier-Stokes (RANS) technology is useful to predict attached flow. But vortex interaction with other vortices and breakdown lead to unsteady, largely separated flow which has been found out of scope for RANS. Direct simulation of the Navier-Stokes equations is out of computational reach in the foreseeable future, and the need for better physical modeling is evident. Both cruise performance and stalling characteristics are influenced by strong interactions. Two important aspects of wing-flow physics are discussed: separation from a smooth surface that creates a vortex, and vortex bursting, the abrupt breakdown of a vortex with a subsequent loss of lift. Vortex aerodynamics of not-so-slender wings encounter particularly challenging problems, and it is shown how the design of early-generation operational aircraft surmounted these difficulties. Through use of forensic CFD, the article concludes with two case studies of aerodynamic design: how the Saab J29A wing maintains control authority near stall, and how the Saab J32 mitigates pitch-up instability at high incidence.