Summary form only given as follows. Explosively driven MCGs were first conceived in the 1950s, with such dignitaries as Max Fowler and Alexander Sakharov claiming credit for the invention. These are essentially high power electrical dynamos that use explosively driven metal armatures to rapidly compress strong magnetic fields. The discharge of large currents from high-energy capacitor banks, is the typical method of generating these magnetic fields, the so-called "seed" fields. Less commonly, other techniques may be used, including explosively shocked sources, and permanent magnets. The basic principle of these devices is that work is done on the seed field by compressing it into a smaller volume. As energy and magnetic flux are conserved, large electrical currents and energies result. The energy efficiency of these devices is comparable to other explosive devices. For example, a shaped charge warhead delivers approximately 5% of the explosive energy to the target. MCGs are typically 5 to 10% efficient, although efficiencies as high as 30% have been claimed. Since explosives are high energetic, >5 MJ/kg being typical, MCGs can provide high energy and power for a variety of applications. Some of the Los Alamos high-energy density physics experiments, which use MCGs, are described. Recent work includes: the generation of 1.5 MJ soft X-rays in a plasma implosion device driven by a call for TW power conditioning system; and the acceleration of solid metal liners to velocities exceeding 18 km/s using currents of 40 MA or more. In other applications, voltages up to 1 MV have been obtained using various power conditioning techniques, e.g., explosively formed fuses and transformers.