This dissertation explains the dynamics of the outer Earth's electron radiation belt during quiet and storm times. Highly energetic electrons in the Earth's radiation belts are hazardous for satellite electronics. Fluxes of relativistic electrons in the outer radiation belt can vary by orders of magnitude during geomagnetic storms. The evolution of relativistic electron fluxes in the radiation belts is described by the 3-D Fokker-Planck equation in terms of the radial distance, energy, and equatorial pitch-angle. In this work, we present a detailed description of the 3-D Versatile Electron Radiation Belt (VERB) code, which is capable of performing radiation belt simulations. The model includes radial, energy, pitch-angle, and mixed energy and pitch-angle diffusion driven by resonant wave-particle interactions with plasma waves inside the magnetosphere. Losses to the atmosphere are accounted for by the simulation of the atmospheric loss cone, while losses to the magnetopause and sources due to magnetospheric convection are accounted for by the boundary conditions. We describe the computationally efficient methods used by the code and the tests we conducted to verify the validity of our numerical approach. With an idealized storm simulation, we show that various diffusion processes are strongly coupled to one another and should be included in realistic simulations of the radiation belts. We show the sensitivity of the simulations to the assumed wave model and input parameters. To study the combined effect of magnetospheric convection and radiation belt diffusion processes, we perform a coupled simulation of the Rice Convection Model (RCM) and the VERB code. This simulation indicates that storm-time enhanced magnetospheric convection combined with radial diffusion can bring electrons with tens of keV energy close to the Earth and can affect electron fluxes at 3-4 R_E. These electrons can be further accelerated locally by chorus waves to MeV energies and transported outward by radial diffusion. This scenario can potentially be a dominant source of the relativistic electrons that are found at geosynchronous orbit. To better understand the mechanisms that controls the radiation belt's particle flux dynamics, we present a 100-day radiation belt simulation that shows good agreement with satellite measurements. Using sensitivity simulations, we show that the model results are very sensitive to the assumed wave model. The VERB simulations are driven only by the Kp index and variations of the seed electron population around geosynchronous orbit, allowing the model to be used for forecasting and now-casting. We also present a numerical solution of the Fokker-Planck equation in terms of the adiabatic invariants using only one numerical grid, which may become standard in future radiation belt models.