The development of high-intensity electromagnets, hand in hand with the development of science, is traced since the discoveries of Oersted, particular emphasis being placed on normal conducting devices both continuously energized and pulsed. Those aspects which most limit the performance of high-intensity electromagnets are reviewed and fundamental limitations, where they exist are pointed out. One of the most important limitations, that of mechanical strength, is treated in some depth, particularly the historical development of stress analysis. Finally, the author discusses the likely impact of magnetic technology, including superconducting technology, upon the future of our society.