The year 2019 marks the 60th anniversary of the concept of radial diffusion in magnetospheric research. This makes it one of the oldest research topics in radiation belt science. While first introduced to account for the existence of the Earth’s outer belt, radial diffusion is now applied to the radiation belts of all strongly magnetized planets. But for all its study and application, radial diffusion remains an elusive process. As the theoretical picture evolved over time, so, too, did the definitions of various related concepts, such as the notion of radial transport. Whether data is scarce or not, doubts in the efficacy of the process remain due to the use of various unchecked assumptions. As a result, quantifying radial diffusion still represents a major challenge to tackle in order to advance our understanding of and ability to model radiation belt dynamics. The core objective of this review is to address the confusion that emerges from the coexistence of various definitions of radial diffusion, and to highlight the complexity and subtleties of the problem. To contextualize, we provide a historical perspective on radial diffusion research: why and how the concept of radial diffusion was introduced at Earth, how it evolved, and how it was transposed to the radiation belts of the giant planets. Then, we discuss the necessary theoretical tools to unify the evolving image of radial diffusion, describe radiation belt drift dynamics, and carry out contemporary radial diffusion research.