Invasive nonnative species acting as “ecosystem engineers” or “geomorphic agents” can represent a major landscape disturbance. Quantification of their biogeomorphic impacts remains a key knowledge gap, and aquatic‐terrestrial transition zones may be particularly exposed to impacts. We demonstrate how burrowing invasive species represent a potentially significant but unquantified erosion risk at aquatic margins. We reveal a lack of quantitative research on geophysical impacts, despite increasing concerns over threats to waterways and flood defense infrastructure. We explore example animals of global interest, comprising crustaceans, fish, reptiles, and mammals and reveal the global nature of the issue: over 100 countries, states, or territories where at least one example species is established, and over 20 with 3‐6 species present. We present a conceptual model for the impacts of burrows on stability and erosion at aquatic margins using established models of geotechnical, hydrological, and hydraulic drivers. Burrows are hypothesized to (i) alter failure plane position, decrease failure plane length, and increase failure plane angle (thereby decreasing bank shear strength); (ii) modify the spatial distribution of porewater pressure, thereby increasing subsurface flow (seepage), reducing cohesion, and increasing the likelihood of slip failures at the bank face; (iii) increase turbulence and sediment entrainment at burrow entrances; and (iv) alter flow resistance at the bank face. Most effects are expected to increase bank instability/erosion with the exception of (iv) which has the potential to offer protection from fluvial action. We call for further research in these areas to quantify impacts for different environments and different invasive species.