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• Key application areas of deep learning are identified in urban water and wastewater management. • Popular application areas include anomaly detection, system state forecasting, asset monitoring and assessment. • Industrial application of deep learning is still at an early stage with few implementations reported. • Research challenges include data privacy, algorithm development, explainability, multi-agent system and digital twin. • Deep learning should drive urban water systems towards high intelligence and autonomy. Deep learning techniques and algorithms are emerging as a disruptive technology with the potential to transform global economies, environments and societies. They have been applied to planning and management problems of urban water systems in general, however, there is lack of a systematic review of the current state of deep learning applications and an examination of potential directions where deep learning can contribute to solving urban water challenges. Here we provide such a review, covering water demand forecasting, leakage and contamination detection, sewer defect assessment, wastewater system state prediction, asset monitoring and urban flooding. We find that the application of deep learning techniques is still at an early stage as most studies used benchmark networks, synthetic data, laboratory or pilot systems to test the performance of deep learning methods with no practical adoption reported. Leakage detection is perhaps at the forefront of receiving practical implementation into day-to-day operation and management of urban water systems, compared with other problems reviewed. Five research challenges, i.e., data privacy, algorithmic development, explainability and trustworthiness, multi-agent systems and digital twins, are identified as key areas to advance the application and implementation of deep learning in urban water management. Future research and application of deep learning systems are expected to drive urban water systems towards high intelligence and autonomy. We hope this review will inspire research and development that can harness the power of deep learning to help achieve sustainable water management and digitalise the water sector across the world. [Display omitted] [ABSTRACT FROM AUTHOR]