Detailed electrodynamic descriptions of the fundamental workings of microwave heating devices are presented. We stress that all results come from Maxwell equations and the boundary conditions (BC). We analyze one by one the principal components of a microwave heater; the cooking chamber, the waveguide, and the microwave sources, either klystron or magnetron. The boundary conditions at the walls of the resonant cavity and at the interface air/surface of the food are given and show how relevant the BC are to understand how the microwaves penetrate the nonconducting, electric polarizable specimen. We mention the application of microwaving waste plastics to obtain a good H2 quantity that could be used as a clean energy source for other machines. We obtained trapped stationary microwaves in the resonant cavity and traveling waves in the waveguides. We show 3D plots of the mathematical solutions and agree quite well with experimental measurements of hot/cold patterns. Simulations for cylindrical cavities are shown. The radiation processes in klystrons and magnetrons are described with some detail in terms of the accelerated electrons and their trajectories. These fields are sent to the waveguides and feed the cooking chamber. Whence, we understand how a meal or waste plastic, or an industrial sample is microwave heated.