Though urban areas represent a small fraction of global land cover, they have an outsized impact on hydrological processes. Within these areas, the pathways that water follows are fundamentally transformed by the disturbance of soils, land cover, vegetation, topography, and built infrastructure. While progress has been made across many cities to quantify interactions between hydrological processes and the urban environment, many fundamental questions remain unanswered. In this article, we review the state of urban hydrologic science, with an eye towards identifying gaps in our understanding of how water flows through built landscapes. Our review focuses on key topics within urban hydrology related to water quantity, including runoff and streamflow generation, soils and soil water, groundwater, vegetation, and climate. We also describe some of the challenges and opportunities within the field of urban hydrology that we envision will drive future work and collaboration.