Non-perennial rivers and streams are ubiquitous on our planet. Although several metrics have been used to statistically group or compare streamflow characteristics, there is currently no widely used definition of how many days or over what reach length surface flow must cease in order to classify a river as non-perennial. At the same time, the breadth of climate and geographic settings for non-perennial rivers leads to diversity in their flow regimes, such as how often or how quickly they go dry. These rivers have a rich and expanding body of literature addressing their ecologic and geomorphic features, but are often said to be ignored by hydrologists. Yet there is much we do know about their hydrology in terms of streamflow generation processes, water losses, and variability in flow. We also know that while they are prevalent in arid regions, they occur across all climate types and experience a diverse set of natural and anthropogenic controls on streamflow. Furthermore, measuring and modeling the hydrology of these rivers presents a distinct set of challenges, and there are many research directions, which still require further attention. Therefore, we present an overview of the current understanding, methodologic challenges, knowledge gaps, and research directions for hydrologic understanding of non-perennial rivers; critical topics in light of both growing global water scarcity and ever-changing laws and policies that dictate whether and how much environmental protection these rivers receive. This article is categorized under: Science of Water > Science of Water.