Modern water distribution networks (WDNs) are complex and difficult to manage due to increased level of urbanization, varying consumer demands, ageing infrastructure, operational costs, and inadequate water resources. The management problems in such complex networks may be classified into short-term, medium-term, and long-term, depending on the duration at which the problems are solved or considered. To address the management problems associated with WDNs, mathematical models facilitate analysis and improvement of the performance of water infrastructure at minimum operational cost, and have been used by researchers, water utility managers, and operators. This paper presents a detailed review of the management problems and essential mathematical models that are used to address these problems at various phases of WDNs. In addition, it also discusses the main approaches to address these management problems to meet customer demands at the required pressure in terms of adequate water quantity and quality. Key challenges that are associated with the management of WDNs are discussed. Also, new directions for future research studies are suggested to enable water utility managers and researchers to improve the performance of water distribution networks.