Foundation scour is one of the primary causes of hydraulic failures in river-crossing bridges. By integrating flume experiments, prototype observations, numerical simulations, and artificial intelligence methods, this study reviews research on foundation scour of river-crossing bridges over the past six decades, summarizes progress in three aspects of general scour, contraction scour, and local scour, analyzes the limitations in existing research, and proposes future research directions. In terms of physical mechanisms, most existing studies focus on bridge foundation scour under simplified boundary conditions such as straight channels, non-cohesive riverbeds, and cylindrical structures. However, cohesive sediments prevalent in natural rivers exhibit complex force interactions and high randomness, resulting in scour processes for bridge foundations that differ significantly from those in non-cohesive riverbeds. Moreover, in common natural channels such as braided, branching, confluence, and alternating wide-narrow channels, water-sediment dynamics and riverbed evolution involve numerous factors with strong uncertainties, making scour mechanisms for bridge foundations more complex than those in straight channels. Therefore, future research must focus on scour mechanisms under more boundary conditions commonly found in natural rivers to improve the theoretical framework for foundation scour of river-crossing bridges. Regarding scour prediction methods, existing research primarily relies on flume experiments and prototype observations of specific bridges. The former’s prediction accuracy is severely affected by scale effects, while the latter has limited applicability. To date, there is a lack of predictive formulas or analytical models that quantitatively consider the scale effects on bridge foundation scour. Data-driven models such as artificial neural networks and deep learning can effectively compensate for the inability of conventional prediction methods for bridge foundation scour to account for complex boundary conditions. In particular, multi-module multilayer perceptrons (multi-module MLPs) can construct hybrid neural networks incorporating physical scour mechanisms, showing great potential in addressing the challenges of predicting scour under complex boundary conditions. In numerical modeling, existing methods are often applicable to low Reynolds number conditions, with insufficient accuracy in capturing turbulence at high Reynolds numbers and absence of standardized grid size criteria. Sediment transport is frequently computed using empirical formulas, and dynamic grid technologies often suffer from low precision. Existing numerical methods exhibit inadequate coupling between turbulence models and sediment transport models. Moreover, current numerical simulations are limited to non-cohesive riverbeds, with few models applicable to cohesive riverbeds and virtually no reported models suitable for stratified riverbeds. Therefore, numerical models for bridge foundation scour require in-depth investigation to address these issues in the future, improving their applicability and reliability under complex boundary conditions. In addition, intensified human interventions—including sand mining, channel regulation, and dam construction—have triggered rapid riverbed degradation in many rivers. These degradation events often occur at scales, rates, and complexity far beyond conventional understanding of general riverbed degradation, resulting in highly destructive and abrupt changes. Future research should systematically investigate riverbed evolution under human disturbances. To build a more comprehensive understanding of foundation scour of river-crossing bridges, future studies should better integrate flume experiments, prototype monitoring, numerical modeling, theoretical analysis, artificial neural networks, and deep learning methods. This will enable systematic investigation of bridge scour under human disturbance and complex boundary conditions, thereby improving the theoretical system and developing more widely applicable and reliable scour design methods.