This lecture reviews the progress made towards releasing energy from the fusion of the light nuclei. To achieve this it is necessary to create an extremely hot plasma containing the light nuclei and to hold this plasma together long enough to obtain a net surplus of energy. The only promising way of confining such a hot plasma for sufficient times and isolating it from material surroundings is by means of magnetic fields. Unfortunately plasmas have shown themselves capable of escaping through magnetic fields by a number of forms of instability. The principles of magnetic confinement of plasmas are discussed and the main types of magnetic traps described. These are the open-ended magnetic bottles (Thetatrons, cusp) in which there is a sharp boundary between plasma and surrounding magnetic field, the open-ended adiabatic magnetic traps (magnetic mirrors) in which the plasma is immersed in a magnetic field, and closed adiabatic traps in which the plasma is immersed in a magnetic field whose lines of force close inside the system (torojdal pinch, Stellarators, etc.). The most important instability has been the interchange driven by charge separation of the plasma components caused by rapid motions of the plasma, as in Thetatrons, or more generally, by unfavourable magnetic field curvature, as in magnetic-mirror traps and in toroidal closed traps. In open-ended systems this instability has been overcome by designing traps with favourable magnetic field curvature (magnetic wells). In closed systems, shear in the magnetic field provides conducting paths which cancel the electric fields set up by charge separation, but this stabilizing effect is offset if the path lengths are too long or the plasma too resistive. More recently, closed systems with average favourable curvature of magnetic field lines have given stability when the connecting lengths between regions of favourable and unfavourable curvature are short enough. Smaller scale instabilities, associated with a variety of electrostatic waves which can propagate in the plasma and interact with groups of particles, are now proving troublesome. These can cause the plasma to diffuse very rapidly through the magnetic fields. Although these instabilities are fairly well understood theoretically, they are not yet controllable experimentally and new experiments using magnetic traps, designed to avoid interchange instabilities, are being used to examine them.