The conversion of kinetic energy into internal energy in high-speed boundary layers creates nonuniform density and viscosity fields, which invalidate many foundational theoretical models of wall-bounded turbulence flow, most notably the incompressible log-law for the mean velocity profile. Modeling and prediction of compressible turbulent boundary layers therefore requires a theoretical means of accounting for fluid property variations, the most famous of which is the so-called “Van Driest transformation” that originated in 1951. This paper sets up the general problem and describes our current theoretical understanding of it, with a focus on developments during the last decade. It also describes applications of the theory to engineering friction estimation methods and the development of wall-models for large eddy simulations.