Artificial Intelligence (AI), Machine Learning (ML), and Deep Learning (DL) are revolutionizing hydrology, driving significant advancements in water resource management, modeling, and prediction. This review synthesizes cutting-edge developments, methodologies, and applications of AI-ML-DL across key hydrological processes. By critically evaluating these techniques against traditional models, we highlight their superior ability to capture complex, nonlinear relationships and adapt to diverse environments. We further explore AI applications in precipitation forecasting, evapotranspiration estimation, groundwater dynamics, and extreme event prediction (floods, droughts, and compound events), showcasing their timely potential in addressing critical water-related challenges. A particular emphasis is placed on Explainable AI (XAI) and transfer learning as essential tools for improving model transparency and applicability, enabling broader stakeholder trust and cross-regional adaptability. The review also addresses persistent challenges, including data limitations, computational demands, and model interpretability, proposing solutions that integrate emerging technologies like quantum computing, the Internet of Things (IoT), and interdisciplinary collaboration. This review charts a strategic course for future research and practice by bridging AI advancements with practical hydrological applications. Our findings highlight the importance of embracing AI-driven approaches for next-generation hydrological modeling and provide actionable understandings for researchers, practitioners, and policymakers. As hydrology faces escalating challenges due to human-induced climate change and growing water demands, the continued evolution of AI-integrated models and innovations in data handling and stakeholder engagement will be imperative. In conclusion, the findings emphasize the critical role of AI-driven hydrological modeling in addressing global water challenges, including climate change adaptation, sustainable water resource management, and disaster risk reduction.