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Traditional massive multiple-input multiple-output (MIMO) information theory adopt non-physically consistent assumptions, including white-noised, scalar-quantity, far-field, discretized, and monochromatic EM fields, which mismatch the nature of the underlying electromagnetic (EM) fields supporting the physical layer of wireless communication systems. To incorporate EM laws into designing procedures of the physical layer, we first propose the novel concept of EM physical layer, whose backbone theory is called EM information theory (EIT). In this article, we systematically investigate the basic ideas and main results of EIT. First, we review the fundamental analytical tools of classical information theory and EM theory. Then, we introduce the modeling and analysis methodologies of EIT, including continuous field modeling, degrees of freedom, and mutual information analyses. Several EIT-inspired applications are discussed to illustrate how EIT guides the design of practical wireless systems. Finally, we point out the open problems of EIT, where further research efforts are required for EIT to construct a unified interdisciplinary theory.