Compressible turbulence has extremely important applications in subsonic, supersonic, and hypersonic aerodynamics. More generally, and even at low Mach numbers, strong density differences caused by intense heating (in combustion for instance) may have profound consequences on the flow structure and the associated mixing. Heating a wall may, for instance, completely destabilize a boundary layer, as will be shown for some applications in this chapter. The chapter is organized as follows. We will first present the compressible LES formalism for an ideal gas in a simple way, allowing us to generalize the use of incompressible subgrid models. This is possible using the concept of density-weighted Favre filtering together with the introduction of a macropressure and a macrotemperature related by the ideal-gas state equation. Then we will study compressible mixing layers at varying convective Mach numbers. Afterward we will consider low or moderate Mach numbers in boundary layers, channel, cavities, and separated flows and also a transonic rectangular cavity. A supersonic application relating to the European space shuttle Hermés rear-flap heating during atmospheric reentry will be discussed in detail. This problem, studied in Grenoble in 1993, has acquired a tragic topicality with the loss of the American Columbia shuttle on February 1, 2003. The latter disintegrated during reentry at an approximate elevation of 60 km and a speed of 21,000 km/h while making a turn at an angle of 57°. It seems that the left wing overheated, possibly because of damage to the protection tiles during takeoff.