This book presents state-of-the-art lectures on complex flows of fundamental and industrial interest in the subsonic, supersonic and hypersonic regimes. Experimental investigations of unsteady separated flows, high-enthalpy flows, 3D configurations, laminar and transitional flows are addressed. Theoretical predictions of aerodynamic performances are provided along with analyses of supersonic combustion, detonation, simulation of reactive mixing layer and non-equilibrium flow. Computational Fluid Dynamics methods for the simulation of viscous compressible flow, inviscid viscous flow interactions, real-gas effects in rarefied flow, flows about bodies with permeable walls and supersonic turbulent flows are finally developed and analysed.