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This tutorial paper deals with several aspects of basic electromagnetic theory that appear to be insufficiently appreciated a century and one-half after Maxwell published his well-known equations, and over a half-century since the MKS/SI system of units was introduced. New concepts have not been completely embraced, while older artifacts and anachronisms have lingered on. The main issues include problems stemming from the original theory of magnetism, confusion between key aspects of the fields B and H, and the somewhat puzzling equivalences between characteristically different mathematical models based on poles or currents. While the answers to most of these questions are somewhere or another in the literature, they are often difficult to find, and there seems to be a lack of a consistent approach to the fundamentals. This article surveys the problem areas, explores the issues involved, and attempts to provide clear answers and understanding through reasoning and commentary. Only simple mathematics has been used, and the treatment has been kept strictly in terms of the field quantities. Results and detailed references are given in key areas, and the history of the subject is touched on where relevant.