Turbulent flows are ubiquitous in most application fields, ranging from engineering to earth sciences and even life sciences. Therefore, the simulation of turbulent flows has become a key tool in both fundamental and applied research. The complexity of Navier-Stokes turbulence renders direct numerical simulations inapplicable to most flows of interest. To alleviate this problem, truncated solutions in both frequency and wavenumber were found. The most suitable approach to obtain such a low-cost three-dimensional unsteady simulation of a turbulent flow is Large-Eddy Simulation (LES), which was pioneered to compute meteorological flows in the late 1950s and the early 1960s. Large Eddy Simulation (LES) of compressible flows is still a widely unexplored area of research. The authors, whose books are considered the most relevant monographs in this field, provide the reader with a comprehensive state-of-the-art presentation of the available LES theory and application. This book is a sequel to Large Eddy Simulation for Incompressible Flows, as most of the research on LES for compressible flows is based on variable density extensions of models, methods and paradigms that were developed within the incompressible flow framework. The book addresses both the fundamentals and the practical industrial applications of LES in order to point out gaps in the theoretical framework as well as to bridge the gap between LES research and the growing need to use it in engineering modeling. 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 implicitmodeling 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.