Today´s propulsion systems are required to produce a larger and more rapid release of energy from smaller and more compact combustors, to cope with the demand for increased speed and range, and a wider operational envelope. For current and future propulsion systems it is therefor important to obtain maximum combustion efficiency and stable operation, to increase the safety, to minimize combustion induced instabilities and to comply with the environmental constraints. Consequently, a thorough understanding of the basic fluid dynamic, thermodynamic and chemical processes involved in combustion becomes a necessity for the construction, operation, maintenance and procurement of efficient and reliable propulsion systems. The following report treats the physical and numerical background for Computational Fluid Dynamic (CFD) modeling of reactive flows and gives a review of non-intrusive experimental techniques for combustion diagnostics that may be used to understand and develop the best operating propulsion system. The main purpose of the report is to give a solid foundation for the continuation of the work in the project "High Speed Combustion."