Nuclear fusion could play a major role in the energy mix during the second half of this century. The advantages of nuclear fusion, in particular for base load power stations, are obvious: the fuel is nearly unlimited and widely available, and - in contrast to fission - there is no possibility of a runaway reaction or meltdown. After more than 50 years of research, fusion has advanced to the decisive step on the way to a power plant: the international tokamak experiment ITER is designed to demonstrate the feasibility of net energy production from nuclear fusion reactions. For a fusion reactor, matter has to be heated up to extremely high temperatures: more than 100 million degrees - about a factor of 10 hotter than the sun's core. At these temperatures the material is fully ionized. The charged particles can be confined by magnetic fields, which are also able to provide the required efficient heat insulation. For magnetic fusion reactions to be self-sustaining, the thermal insulation has to be a factor of 100 better than that of polystyrene - at temperatures, where the velocity of particles approaches one fifth of the velocity of light! The physics basis of such magnetic confinement will be discussed. The two alternative concepts on the way to a fusion power plant: the tokamak and the stellarator will be introduced and the remaining scientific challenges for magnetic fusion will be discussed.