IntroductionThe impact of microwave (MW) irradiation in organic synthesis has increased over the years and especially since the development of new dedicated and reliable MW instruments [1].MW-assisted organic synthesis has been characterized by the spectacular accelerations produced in many reactions as a consequence of a heating rate which, in most cases, cannot be reproduced by classical heating. This effect is particularly important in (i) the preparation of isotopically labeled drugs for positron emission tomography (PET) that have a short half-life ( 11 C, t1 / 2 = 20 min; 122 I, t1 / 2 = 3.6 min; 18 F, t1 / 2 = 100 min) [2], (ii) high-throughput chemistry (combinatorial and parallel chemistry) where a rapid synthesis may increase the efficiency [3], (iii) catalysis where the short reaction time protects the catalyst from decomposition and increases the catalyst efficiency [4], and (iv) the synthesis of unstable or sensitive compounds, for example, natural products, where the short reaction time prevent the decomposition that occurs with long reaction times [5].The occurrence of results that cannot be explained exclusively by rapid heating led several authors to postulate the existence of a so-called ''microwave effect.'' Hence acceleration or modifications of the selectivity and reactivity could be explained by an effect of the electromagnetic radiation and not merely by the heating effect. In this way, in combination with the rapid heating, specific thermal effects and non-thermal effect could be the responsible for the improvement of many chemical processes.The occurrence of MW effects has been the subject of much controversy. In this chapter, we describe the state-of-the-art of this subject and we present many examples in favor of and against the presence of MW effects with a critical appraisal.Microwaves in Organic Synthesis, Third Edition.