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Abstract: After the discovery of the Van Allen radiation belts over 60 years ago, processes responsible for the transport, loss, and energization of the relativistic electrons in the belts have been one of the most actively researched topics in the space physics community. Current understanding is that the trapped electrons can be either lost to the atmosphere because of the interaction with high-frequency plasma waves such as whistler mode chorus, plasmaspheric hiss, or electromagnetic ion cyclotron waves, or they can be transported outward to the magnetopause and lost to the magnetosheath because of their interaction with ultra-low frequency (ULF) waves. However, both of these approaches fail to explain the observations of extremely fast radiation belt losses with timescales of ~0.5-2 hours. This thesis is focused on the analysis of such extremely fast radiation belt extinction events. Specifically, we try to determine if the outer radiation belt response and the magnetosphere dynamics fit within the outward ULF wave radial diffusion paradigm. Firstly, we analyze Pc4-Pc5 ULF wave dynamics in the electromagnetic field of the Earth during the intense geomagnetic storm on March 17-18, 2015. This storm is a classic example of a radiation belt extinction event, during which the population of ultra-relativistic electrons was lost within 2 hours after the storm commencement. Analysis of measurements of the electromagnetic field from GOES and THEMIS satellites and ground-based magnetometers shows that the main phase storm-specific ULF waves do not correspond to statistical estimates. Notably, the radial diffusion rates produced by the electric field are reduced, compared to empirical models based on Kp. Meanwhile, the magnetic diffusion rates are increased. Our results show that the main phase magnetic radial diffusion cannot be neglected, contrary to prior results. Therefore, to accurately represent the diffusion rates during such fast loss events, and which we further show are associated with periods characterized by a strong southward component of the interplanetary magnetic field, modifications of the statistical Kp-dependent models for the ULF wave radial diffusion coefficients are required. Secondly, we use electron flux data from the constellation of Global Positioning System (GPS) satellites to resolve the fast timescale characteristics of the radiation belt response during radiation belt extinction events. We investigate storms that happened between 2012 and 2015 with different loss and recovery patterns. We compare the dynamics of the outer radiation belt with the last closed drift shell (LCDS), computed using the Tsyganenko2005 magnetic field model, and the results show a very strong correspondence between the two. Significantly, the location of the LCDS closely mirrors the high time resolution losses observed in GPS flux. We conclude that expressing the location of the LCDS in L* space and using the electron flux observations from the GPS satellites are crucial when addressing the rapid relativistic electron flux loss associated with magnetopause shadowing. Finally, we perform a statistical analysis of the trapped electron radiation during magnetopause shadowing events. We use a superposed epoch analysis of ultra-relativistic electron flux data and additionally compute phase space density from the Van Allen Probes to analyze 64 magnetopause shadowing events from 2012 until 2018. Our analysis confirmed that magnetopause shadowing losses can occur on the timescales of