Many desirable organic reactions are accompanied by side reactions and undesired by-products, which waste raw materials and complicate product work-up and isolation. By enhancing the competition between reactions to obtain more selective syntheses, ecological and economic benefits may be expected. The most effective way to do this is usually catalysis. Recently, however, more has been learned about the role of "reactive mixing", which refers here to bringing reagents together on the molecular scale. When chemical knowledge (especially reaction kinetics and physical organic chemistry) is combined with that of mixing, significant improvements to the selectivity of some syntheses can be achieved. This review offers an introduction to understanding how mixing influences those single-phase and two-phase reactions which are sufficiently fast that mixing cannot fully homogenize their reactants. It includes theoretical principles, typical experimental results, worked examples, and literature references for further study. Reactive mixing is treated in very few textbooks (refer to section 1), is unknown to many chemists, and is unfamiliar to many chemical engineers. It is hoped that its wider recognition will lead others to become intellectually fascinated by its structure and to value its practical applications.