The review is concerned with models that analyze transport:processes that occur during microwave heating. Early models on microwave. heating used Lambert＇s law to describe the microwave power absorption. Over the last decade, models for transport processes have been developed with the microwave power derived from Maxwell＇s equations. Those models, primarily based on plane waves, have been used for analyzing microwave heating of solids, liquids, emulsions, microwave thawing and drying. The models illustrate phenomena such a resonances, hot spots, edge and runaway heating. The literature on microwave sintering, susceptor heating and microwave assisted synthesis is largely experimental in nature and only key issues are highlighted. To fully appreciate the models for microwave heating, a section on the theory of electromagnetic wave propagation is included, where expressions for the electric field in dielectric slabs and cylinders are presented.