Microwave irradiation has been successfully applied in organic chemistry. Spectacular accelerations, higher yields under milder reaction conditions and higher product purities have all been reported. Indeed, a number of authors have described success in reactions that do not occur by conventional heating and even modifications of selectivity (chemo-, regio- and stereoselectivity). The effect of microwave irradiation in organic synthesis is a combination of thermal effects, arising from the heating rate, superheating or "hot spots" and the selective absorption of radiation by polar substances. Such phenomena are not usually accessible by classical heating and the existence of non-thermal effects of highly polarizing radiation--the "specific microwave effect"--is still a controversial topic. An overview of the thermal effects and the current state of non-thermal microwave effects is presented in this critical review along with a view on how these phenomena can be effectively used in organic synthesis.