This chapter mainly provides an insightful review and reinforcement of the key concepts of one-dimensional compressible flows with area change, friction, heat transfer, and rotation. The fluid density is no longer a constant, as in an incompressible flow, but changes with pressure and temperature. Mach number plays a key role in characterizing compressible flows: the higher the Mach number, the higher the flow compressibility with two-way exchange between internal and external flow energies. Although the fluid in a compressible flow must always be compressible, like air or other gases, such a flow may be treated as incompressible for Mach numbers less than 0.3. In compressible flows, the entropy considerations to satisfy the second law of thermodynamics become necessary to screen out solutions that are physically impossible. In addition to many one-dimensional flows, the chapter also discusses the key features of a couple of two-dimensional flows such as oblique shock waves, which are non-isentropic, and Prandtl-Meyer expansion waves, which are isentropic.