Despite the importance of rivers to industry, agriculture, the climate system, and global ecosystems, our current knowledge of river discharge (volume of available water per unit time) is surprisingly poor for many regions of the world as political cloistering, aging infrastructure, and rapid human changes limit our ability to understand global surface waters holistically. Closing this knowledge gap is critical for better management of surface water in light of drought and increasing human demand for fresh water, especially as the earth’s hydrological system responds to a changing climate. Nowhere on earth is this hydrologic uncertainty more acute than the Arctic, where already difficult-to-obtain in situ observations have declined in recent decades and where rising air, soil, and water temperatures exert outsized impact on natural systems. Furthermore, even basic fluvial science is underdeveloped in the Arctic, as routine field measurements are logistically challenging and sometimes dangerous to obtain. To these ends, this dissertation seeks to combat these global hydrologic challenges, and is centered on rivers at the intersection between geography, fluvial hydrology, and geomorphology. Specifically, this dissertation asks and answers three interconnected questions that I believe are critical for improved scientific understanding of global and Arctic hydrology: (1) Can river flows and freshwater resources be quantified globally, even in remote and/or politically sensitive regions? (2) What can we learn about rivers by thinking about them spatially? (3) How do rivers of the cryosphere differ from their better-studied temperate counterparts? The work herein is built on extensive field work, satellite remote sensing, modeling, and GIS, and contains seven chapters. This document compiles original information about the geomorphology of rivers (that is, how they shape and are shaped by the landscape, Chapters 1, 2, 4, and 7) and applies that knowledge to develop a novel methodology for estimating river discharge from remotely sensed imagery (Chapters 2, 3, and 6). Building on this work, this document also critically considers how these methods might influence local politics (Chapter 5). In sum, this document represents an attempt to holistically understand rivers from numerous vantage points, and succeeds in reveling previously undiscovered river behavior by applying a geospatial paradigm to fluvial science.