Small fluctuations in magnetospheric electric and magnetic fields lead to random changes in the radial positions of trapped particles. The characteristics of this radial diffusion are described theoretically in terms of the statistical properties of the field fluctuations, in particular the power spectra of the various spatial components. A large body of trapped particle data demonstrates that diffusion with the predicted properties actually takes place. These data include the average radial and energy distributions and the time variations in particle fluxes. This radial diffusion has a major influence on the structure of the radiation belts; and since the net flow of particles is inward at most positions of the magnetosphere, the process acts as a strong source of trapped particles. Further experiments are needed to establish the importance of this mechanism relative to magnetic storm effects and to collective instabilities.