Numerous arrangements for permanent magnets are disclosed that can focus the flux produced by the magnets. Depending on the particular application in which the disclosed designs and techniques are used, efficiency and reliability may be increased by minimizing flux leakage, increasing peak flux density, and shaping the flux fields to improve the effective coercivity of the flux focusing permanent magnet arrangement when loaded, and to achieve customized voltage and current waveforms. The disclosed magnet assemblies may be incorporated into a machine, such as a motor/generator, having windings and may be disposed for movement relative to the windings. The magnet assembly may be mounted on a support formed of one or more ferromagnetic materials, such as a back iron. The disclosed flux focusing magnet assemblies may be formed using a variety of manufacturing methods.