Abstract-Potable water distribution networks (WDNs) and wastewater collection networks (WWCNs) are the two fundamental constituents of the complex urban water infrastructure. Such water networks require adapted design interventions as part of retrofitting, extension and maintenance activities. Consequently, proper optimization methodologies are required to reduce the associated capital cost while also meeting the demands of acquiring clean water and releasing wastewater by consumers. In this paper, a systematic review of the optimization of both WDNs and WWCNs, from the preliminary stages of development through to the state-of-the-art, is jointly presented. Firstly, both WDNs and WWCNs are conceptually and functionally described along with illustrative benchmarks. The optimization of water networks across both clean and waste domains is then systematically reviewed and organized, covering all levels of complexity from the formulation of cost functions and constraints, through to traditional and advanced optimization methodologies. The rationales behind employing these methodologies as well as their advantages and disadvantages are investigated. The paper then critically discusses current trends and identifies directions for future research by comparing the existing optimization paradigms within WDNs and WWCNs and proposing common research directions for optimizing water networks. Optimization of urban water networks is a multidisciplinary domain, within which this paper is anticipated to be of great benefit to researchers and practitioners.