Lectures will attempt to offer an historical perspective on the progress in this field underlining the knowledge and methods that were borrowed from the incompressible regime.The concept of averaging and filtering techniques will be addressed. Advances in non-intrusive and intrusive experimental techniques will be proposed. An up-to-date review of the turbulence modeling involving the RANS and LES approaches will be presented. Comparison/validation with existing Direct Numerical Simulations will be commented. A review of fundamental configurations such as the shock turbulence interaction, the shock boundary layer interaction or the transition from laminar to turbulence will be done.