Chemical kinetic modeling of high temperature hydrocarbon oxidation in combustion is reviewed. First, reaction mechanisms for specific fuels are discussed, with emphasis on the hierarchical structure of reaction mechanisms for complex fuels. The concept of a comprehensive mechanism is developed, requiring model validation by comparison with data from a wide range of experimental regimes. Fuels of increasing complexity from hydrogen to n-butane are described in detail, and further extensions of the general approach to other fuels are discussed. Kinetic modification to fuel oxidation kinetics is considered, including both inhibition and promotion of combustion. Simplified kinetic models are then described by comparing their features with those of detailed kinetic models. Finally, application of kinetic models to study real combustions systems are presented, beginning with purely kinetic-thermodynamic applications, in which transport effects such as diffusion of heat and mass can be neglected, such as shock tubes, detonations, plug flow reactors, and stirred reactors. Laminar flames and the coupling between diffusive transport and chemical kinetics are then described, together with applications of laminar flame models to practical combustion problems.