In theoretical work beginning in the 1990s, O'Shaughnessy and co-workers predicted that for lateral diffusion at a solid-liquid interface, a key step involves desorption, excursion through the liquid phase, and readsorption to the interface. This step was expected to dominate twodimensional surface diffusion over certain time scales, leading to anomalous diffusion; in practice, such liquid-phase excursions could significantly impact the efficiency and kinetics of interfacial processes. In this contribution, we emphasize the application of single-molecule methods in exploring the characteristics, influential factors, mechanisms, and consequences of anomalous interfacial diffusion and discuss possible ways to control the elementary processes of desorption-mediated anomalous diffusion. It is hoped that the insights provided from understanding these elementary processes will enable researchers to exploit and control intermittent hopping in applications involving interfacial diffusion, such as surface reactions, molecular recognition, and surface biocompatibility.