Compressible flows are considered in this chapter. Methods designed for compressible flows are briefly discussed. The extension of pressure-correction approaches based on the fractional-step method and the SIMPLE algorithm for incompressible flows to compressible flows is described in more detail. Methods for dealing with shocks (e.g., grid adaptation, total-variation-diminishing and essentially-non-oscillating schemes) are also discussed. Boundary conditions for various types of compressible flows (subsonic, transonic and supersonic) are described. Finally, application examples are presented and discussed.