Water distribution networks (WDNs) are critical contributors to the social welfare, economic growth, and public health in cities. Under the uncertainties that are introduced owing to climate change, urban development, aging components, and interdependent infrastructure, the WDN performance must be evaluated using continuously innovative methods and data acquisition. Quantitative resilience assessments provide useful information for WDN operators and planners, enabling support systems that can withstand disasters, recover quickly from outages, and adapt to uncertain environments. This study reviews contemporary approaches for quantifying the resilience of WDNs. 1508 journal articles published from 1950 to 2018 are identified under systematic review guidelines. 137 references that focus on the quantitative resilience methods of WDN are classified as surrogate measures, simulation methods, network theory approaches, and fault detection and isolation approaches. This study identifies the resilience capability of the WDNs and describes the related terms of absorptive, restorative, and adaptive capabilities. It also discusses the metrics, research progresses, and limitations associated with each method. Finally, this study indicates the challenges associated with the quantification of WDNs that should be overcome for achieving improved resilience assessments in the future.