This paper reviews the status of radiation belt science at the close of the data acquisition phase (1976–1979) of the International Magnetospheric Study. The purpose is to place recent discoveries in context with respect to long‐standing problems and to indicate possible directions for future research in radiation belt physics. The review includes a synopsis of results achieved on topics related to the source, energization, transport, and loss processes for geomagnetically trapped radiation, as well as results concerning certain subtle consequences of adiabatic charged particle motion. Major areas of interest include the effects of charge exchange and radial transport on the ion composition of the ring current and radiation belts, the measurement of ion distributions in all three dimensions of velocity space, and the evolution of radiation belt particle intensities as a consequence of temporal variations of transport coefficients and boundary conditions over the solar cycle and over the course of a magnetic storm. The realization is gradually developing that the major uncertainties in radiation belt physics lie beyond the radiation belts themselves. These uncertainties include (1) the problem of particle energization in the plasma sheet, which defines an outer boundary condition for the ring current and radiation belts, (2) the problem of particle energization in solar flares and in Jupiter's magnetosphere, both of which constitute possible sources for the earth's radiation belts, and (3) the relationship of large‐scale electric and magnetic field fluctuations across the magnetosphere to interplanetary parameters and geomagnetic indices that vary with time.