After introducing the fundamentals on compressible turbulence and the LES governing equations, the mathematical framework for the filtering paradigm of LES for compressible flow equations is established. Instead of providing the reader with a general discussion about compressibility effects on turbulence, the emphasis is put on differences in scale interactions compared to the incompressible case. Functional modeling is discussed, including a brief introduction into implicit modeling from the functional perspective. The description of explicit structural modeling contains different models based on the scale-similarity hypothesis, on approximate deconvolution, and on multi-resolution concepts to reconstruct the subgrid-scale field. A central part of the monograph is the discussion of numerical methods in relation to LES. After evaluating boundary conditions for LES of compressible flows, which are much more complex than its counterpart for incompressible flows, the last chapters are dedicated to specific applications to sub- and supersonic flows, including a discussion of shock-related problems.