Although superconductivity will never produce energy by itself, it plays an important role in energy-related applications both because of its saving potential (e.g., power transmission lines and generators), and its role as an enabling technology (e.g., for nuclear fusion energy). The superconducting magnet’s need for plasma confinement has been recognized since the early development of fusion devices. As long as the research and development of plasma burning was carried out on pulsed devices, the technology of superconducting fusion magnets was aimed at demonstrations of feasibility. In the latest generation of plasma devices, which are larger and have longer confinement times, the superconducting coils are a key enabling technology. The cost of a superconducting magnet system is a major portion of the overall cost of a fusion plant and deserves significant attention in the long-term planning of electricity supply; only cheap superconducting magnets will help fusion get to the energy market. In this paper, the technology challenges and design approaches for fusion magnets are briefly reviewed for past, present, and future projects, from the early superconducting tokamaks in the 1970s, to the current ITER (International Thermonuclear Experimental Reactor) and W7-X projects and future DEMO (Demonstration Reactor) projects. The associated cryogenic technology is also reviewed: 4.2 K helium baths, superfluid baths, forced-flow supercritical helium, and helium-free designs. Open issues and risk mitigation are discussed in terms of reliability, technology, and cost.