Planetary magnetospheres are the laboratories of the space plasma physicist, formed by the interaction of the supersonic magnetized solar wind plasma with the ionospheres and intrinsic magnetospheres of the planets. Planets such as Venus and Mars, which have insignificant, if any, internally generated magnetic fields, deflect the incident solar wind with the pressures of their ionospheres forming an induced magnetosphere, somewhat akin to the magnetic structure of a comet. The Earth and Mercury and the Jovian planets have intrinsic magnetic fields of sufficient strength to stand off the solar wind flow well above both the surfaces and atmospheres of these planets. Whether induced or intrinsic these magnetospheres are filled with a myriad of plasma physical phenomena which control the momentum and energy transfer in these systems. This review examines the nature of these magnetospheres, the physical processes occurring therein and the outstanding problems at each planet.