Our modern society requires environmentally friendly solutions for energy production. Energy can be released not only from the fission of heavy nuclei but also from the fusion of light nuclei. Nuclear fusion is an important option for a clean and safe solution for our long-term energy needs. The extremely high temperatures required for the fusion reaction are routinely realized in several magnetic-fusion machines. Since the early 1990s, up to 16 MW of fusion power has been released in pulses of a few seconds, corresponding to a power multiplication close to break-even. Our understanding of the very complex behaviour of a magnetized plasma at temperatures between 150 and 200 million °C surrounded by cold walls has also advanced substantially. This steady progress has resulted in the construction of ITER, a fusion device with a planned fusion power output of 500 MW in pulses of 400 s. ITER should provide answers to remaining important questions on the integration of physics and technology, through a full-size demonstration of a tenfold power multiplication, and on nuclear safety aspects. Here we review the basic physics underlying magnetic fusion: past achievements, present efforts and the prospects for future production of electrical energy. We also discuss questions related to the safety, waste management and decommissioning of a future fusion power plant. One way of realizing controlled nuclear fusion reactions for the production of energy involves confining a hot plasma in a magnetic field. Here, the physics of magnetic-confinement fusion is reviewed, focusing on the tokamak and stellarator concepts.