Microwave heating is caused by the ability of the materials to absorb microwave energy and convert it to heat. This article represents a review on fundamentals of microwave heating and their interaction with materials for various applications in a comprehensive manner. Experimental studies of single, multimode, and variable frequency microwave processing were reviewed along with their applications. Modeling of microwave heating based on Lambert's law and Maxwell's electromagnetic field equations have also been reviewed along with their applications. Modeling approaches were used to predict the effect of resonances on microwave power absorption, the role of supports for microwave heating, and to determine the nonuniformity on heating rates. Various industrial applications on thermal processing have been reviewed. There is tremendous scope for theoretical and experimental studies on the athermal effects of microwaves. Some of the unresolved problems are identified and directions for further research are also suggested. © 2011 American Institute of Chemical Engineers (AIChE).