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Electromagnetic (EM) composites have stimulated tremendous fundamental and practical interests owing to their flexible electromagnetic properties and extensive potential engineering applications. Hence, it is necessary to systematically understand the physical mechanisms and design principles controlling EM composites. In this tutorial, we first provide an overview of the basic theory of electromagnetism about electromagnetic constitutive parameters that can represent the electromagnetic properties of materials. We show how this corpus allows a consistent construction of effective medium theories and allows for numerical simulation of EM composites to deal with structure-property relationships. We then discuss the influence of spatial dispersion of shaped inclusions in the material medium on the EM properties of composites, which has not been systematically illustrated in the context of this interdisciplinary topic. Next, artificial composites or metamaterials with peculiar properties not readily available in nature are highlighted with particular emphasis on the control of the EM interaction with composites. We conclude by discussing appropriate methods of electromagnetic measurement and practical aspects for implementing composites for specific applications are described. Overall, this tutorial will serve the purpose of introducing the basics and applications of electromagnetic composites to newcomers in this field. It is also anticipated that researchers from different backgrounds including materials science, optics, and electrical engineering can communicate to each other with the same language when dealing with this interdisciplinary subject and further push forward this advancement from fundamental science to technological applications.