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Many spacecraft fly within or through a natural and variable particle accelerator powered by the coupling between the magnetosphere and the solar wind: the Earth’s radiation belts. Determining the dominant pathways to plasma energization is a central challenge for radiation belt science and space weather alike. Inward radial transport from an external source was originally thought to be the most important acceleration process occurring in the radiation belts. Yet, when modeling relied on a radial diffusion equation including electron lifetimes, notable discrepancies in model-observation comparisons highlighted a need for improvement. Works by Professor Richard M. Thorne and others showed that energetic (hundreds of keV) electrons interacting with whistler-mode chorus waves could be efficiently accelerated to very high energies. The same principles were soon transposed to understand radiation belt dynamics at Jupiter and Saturn. These results led to a paradigm shift in our understanding of radiation belt acceleration, supported by observations of a growing peak in the radial profile of the phase space density for the most energetic electrons of the Earth’s outer belt. Yet, quantifying the importance of local acceleration at the gyroscale, versus large-scale acceleration associated with radial transport, remains controversial due to various sources of uncertainty. The objective of this review is to provide context to understand the variety of challenges associated with differentiating between the two main radiation belt acceleration processes: radial transport and local acceleration. Challenges range from electron flux measurement analysis to radiation belt modeling based on a three-dimensional Fokker-Planck equation. We also provide recommendations to inform future research on radiation belt radial transport and local acceleration.