We review the experimental and theoretical work which has been carried out on the dynamics of reactions of O(3P) with saturated hydrocarbons and related systems. We concentrate primarily on gas phase reactions, but also cover in less detail the more limited work on condensed phase and interfacial reactions. Although O(3P) + saturated alkane reactions are the primary focus, the dominant features of their dynamics are compared and contrasted with those of unsaturated alkanes, functionalised alkanes, and inorganic hydrides (including silanes, germanes, H2S, and hydrogen halides). The principal experimental techniques are reviewed. The experimentally determined quantities are identified, including excitation functions, OH rovibrational and fine-structure partitioning, the rather limited equivalent results for the organic radical co-product, and differential cross-sections. The dynamical conclusions that have been inferred are discussed and compared with the predictions of various levels of theory from semi-empirical models through to rigorous ab initio treatments. For many organic systems, most of the evidence points to OH being formed via a direct abstraction mechanism in which the O(3P) atom attacks along an isolated C–H bond. Outstanding problems with this basic interpretation and gaps in the current knowledge base are identified.