Microwave- and microwave vacuum-drying processes for the drying of food are described. Starting with some historical remarks on the development of thermal microwave processes, the physical basics of electromagnetism, heat- and mass transfer as well as the important physical properties are specified. Different approaches for the physical description and modeling of microwave processes which are found in literature are shown. After a classifying of industrial microwave dryers some examples of today's microwave drying applications are depicted. The paper should also be a starting point for researchers being interested in detail information on microwave drying applications.