This review of the role of reaction kinetics in combustion chemistry traces the historical evolution and present state of qualitative and quantitative understanding of a number of reaction systems. Starting from the H-2-O-2 system, in particular from the reaction between H and O-2, mechanisms and key reactions for soot formation, for the appearance of NO,, and for processes of peroxy radicals in hydrocarbon oxidation are illustrated. The struggle for precise rate constants on the experimental and theoretical side is demonstrated for the example of the reaction H + O-2 -> OH + O. The intrinsic complexity of complex-forming bimolecular reactions, such as observed even in this reaction, also dominates most other key reactions of the systems considered and can be unravelled only with the help of quantum-chemical methods. The multi-channel character of these reactions often also requires the combination with master equation codes. Although kinetics provides an already impressive database for quantitative modelling of simple combustion systems, considerable effort is still required to quantitatively account for the complexities of more complicated fuel oxidation processes. (c) 2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved.