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Driven by the need for integrated management of groundwater (GW) and surface water (SW), quantification of GW–SW interactions and associated contaminant transport has become increasingly important. This is due to their substantial impact on water quantity and quality. In this review, we provide an overview of the methods developed over the past several decades to investigate GW–SW interactions. These methods include geophysical, hydrometric, and tracer techniques, as well as various modeling approaches. Different methods reveal valuable information on GW–SW interactions at different scales with their respective advantages and limitations. Interpreting data from these techniques can be challenging due to factors like scale effects, heterogeneous hydrogeological conditions, sediment variability, and complex spatiotemporal connections between GW and SW. To facilitate the selection of appropriate methods for specific sites, we discuss the strengths, weaknesses, and challenges of each technique, and we offer perspectives on knowledge gaps in the current science. 

Abstract Hydrologically mediated hot moments (HM‐HMs) of transient anomalous diffusion (TAD) denote abrupt shifts in hydraulic conditions that can profoundly influence the dynamics of anomalous diffusion for pollutants within heterogeneous aquifers. How to efficiently model these complex dynamics remains a significant challenge. To bridge this knowledge gap, we propose an innovative model termed “the impulsive, tempered fractional advection‐dispersion equation” (IT‐fADE) to simulate HM‐HMs of TAD. The model is approximated using an L1‐based finite difference solver with unconditional stability and an efficient convergence rate. Application results demonstrate that the IT‐fADE model and its solver successfully capture TAD induced by hydrologically trigged hot phenomena (including hot moments and hot spots) across three distinct aquifers: (a) transient sub‐diffusion arising from sudden shifts in hydraulic gradient within a regional‐scale alluvial aquifer, (b) transient sub‐ or super‐diffusion due to convergent or push‐pull tracer experiments within a local‐scale fractured aquifer, and (c) transient sub‐diffusion likely attributed to multiple‐conduit flow within an intermediate‐scale karst aquifer. The impulsive terms and fractional differential operator integrated into the IT‐fADE aptly capture the ephemeral nature and evolving memory of HM‐HMs of TAD by incorporating multiple stress periods into the model. The sequential HM‐HM model also characterizes breakthrough curves of pollutants as they encounter hydrologically mediated, parallel hot spots. Furthermore, we delve into discussions concerning model parameters, extensions, and comparisons, as well as impulse signals and the propagation of memory within the context of employing IT‐fADE to capture hot phenomena of TAD in aquatic systems.