Leak management in water distribution networks (WDNs) is essential for minimising water loss, improving operational efficiency, and supporting sustainable water management. However, effectively identifying, preventing, and locating leaks remains a major challenge owing to the ageing infrastructure, pressure variations, and limited monitoring capabilities. Leakage management generally involves three approaches: leakage assessment, detection, and prevention. Traditional methods offer useful tools but often face limitations in scalability, cost, false alarm rates, and real-time application. Recently, artificial intelligence (AI) and machine learning (ML) have shown growing potential to address these challenges. Deep Reinforcement Learning (DRL) has emerged as a promising technique that combines the ability of Deep Learning (DL) to process complex data with reinforcement learning (RL) decision-making capabilities. DRL has been applied in WDNs for tasks such as pump scheduling, pressure control, and valve optimisation. However, their roles in leakage management are still evolving. To the best of our knowledge, no review to date has specifically focused on DRL for leakage management in WDNs. Therefore, this review aims to fill this gap and examines current leakage management methods, highlights the current role of DRL and potential contributions in the water sector, specifically water distribution networks, identifies existing research gaps, and outlines future directions for developing DRL-based models that specifically target leak detection and prevention.