Scientific machine learning (SciML) provides a structured approach to integrating physical knowledge into data-driven modeling, offering significant potential for advancing hydrological research. In recent years, multiple methodological families have emerged, including physics-informed ML, physics-guided ML, explicit physics-ML coupling, and data-driven physics discovery. Within each of these families, a proliferation of heterogeneous approaches has grown up independently, often lacking conceptual coordination. This fragmentation complicates the assessment of methodological novelty and makes it difficult to identify where meaningful advances can still be made in the absence of a unified conceptual framework. This review, the first focused overview of SciML in hydrology, addresses these limitations by proposing a unified methodological framework for each SciML family, bringing together representative contributions into a coherent structure that fosters conceptual clarity and supports cumulative progress in hydrological modeling. Finally, the limitations and future opportunities of each unified family were highlighted to guide systematic research in hydrology, where these methods remain underutilized. This review advances hydrology by unifying fragmented SciML approaches into coherent frameworks, projecting a trajectory of improved predictive power and physical consistency for applications such as flood forecasting and groundwater modeling, while guiding future research to systematically integrate data-driven and physics-based methods to address complex hydrological challenges.