Geomagnetic activity is capable of dramatically affecting the relativistic electrons that comprise the outer zone of the Van Allen radiation belts, with approximately half of geomagnetic storms producing enhancements in the intensity of radiation in the belts, and the remainder either reducing relativistic electron fluxes or having no overall effect. Which of these outcomes will result from any given storm depends on a delicate balance between sources and losses of energy and particles in the system. In this seminar we look at recent work undertaken at LASP on the effects of continuous, low-frequency magnetospheric pulsations on the dynamics of the radiation belts. In particular, we examine the origin and effect of global ULF oscillations in the Pc-5 (mHz) frequency spectrum, and discuss their potential to act as either a source of transport and energy in the radiation belts, or to act as a loss process depleting the energetic electron fluxes in the radiation belts. We also examine the origin and evolution of a second class of ULF oscillations, Pc-1 (kHz) pulsations, which are related to Electromagnetic Ion Cyclotron (EMIC) activity in the magnetosphere and generally act to remove energy and particles from the radiation belts. Finally, we look at global radiation belt dynamics as it may be seen from the upcoming NASA Radiation Belt Storm Probes (RBSP) mission, under differing assumptions of ULF wave activity and source populations in the magnetosphere.