“Non-local” mathematics—which describe longer-range dependencies in time or space than classical, local mathematics—are important in a broad range of scientific disciplines. In groundwater hydrology, for example, one prediction challenge described by non-local mathematics is “anomalous” solute-transport behavior, defined by characteristics such as concentration rebound, solute retention, early solute breakthrough, and long breakthrough tailing. These behaviors lead to consequences like poor 1) pump-and-treat efficiency, 2) descriptions of mixing or spreading, and 3) prediction of biogeochemical storage, release, and transformation processes. These phenomena have been observed in diverse geologic settings. Observational challenges and the complexity of subsurface systems lead to severe prediction challenges with standard measurement techniques. Here, I explore the role of electrical geophysics in determine parameters controlling anomalous solute transport behavior and its applications in a variety of hydrologic settings.