Hydrology is recognised as an important component of the glacial system in alpine environments. In particular, the subglacial drainage of surface meltwaters is known to exert a strong influence on the motion of glaciers and on their capacity to erode the underlying bedrock. This thesis examines the more poorly understood drainage system of the Greenland Ice Sheet, with specific focus on Leverett Glacier, a landterminating outlet glacier on the ice sheet’s western margin. Because of the vast size of the ice sheet, the influence of the drainage system could have wide ranging implications, most notably for sea level rise and continental scale landscape evolution. The thesis commences with an investigation into the morphology of the drainage system of the lower 14 km of Leverett Glacier. This is undertaken using a variety of field methods, including dye tracing and the monitoring of proglacial discharge, englacial water levels, surface melt rates and glacier motion. The data reveal that the drainage system of the glacier closely resembles that of alpine glaciers, undergoing an evolution from distributed to channelised drainage morphologies as the melt season progresses. Another aspect of the field data, the suspended sediment load evacuated from the subglacial system in the emerging proglacial river, is then examined to investigate the impact that this drainage system morphology has on the interaction between the glacier and the underlying bedrock or substrate. This demonstrates that the presence of large, efficient subglacial drainage channels allows for the removal of vast quantities of basal debris during much of the melt season, facilitating an erosion rate 1-2 orders of magnitude greater than previously proposed for ice sheet settings. The thesis then focuses on the relationship between discharge, water pressure and ice motion. Observations from Greenlandic and alpine glaciers demonstrate that glaciers generally decelerate through the melt season following a maximum velocity induced by the onset of melt in the spring. The data indicate that the evolution of the drainage system from a distributed to a channelised morphology occurs rapidly and so can only explain this trend in ice velocity during the early part of the melt season. Beyond this period, ice velocity patterns can instead be explained primarily by transient fluctuations in water pressure within the channelised drainage system. These transient pressure fluctuations result from the lag between changes to the rate of meltwater input to the glacier and the subsequent adjustment of channel cross section. This indicates that it is crucial to consider temporal variability in melt rate when seeking to link climate with the dynamics of ice sheets and glaciers. This process can be simulated, which is demonstrated by using the proglacial discharge record to model subglacial water pressure and ice velocity. In the following chapter, this model is built upon by considering how these variations in water pressure, originating in discrete subglacial channels, control sliding velocities across large areas of the glacier. Detailed examination of high-resolution ice velocity records from Leverett Glacier reveals that, in keeping with theory, horizontal ice velocity is dependent on both the volume of subglacial cavities and the rate-of-change of this volume. A simple model of subglacial water movement is then used to demonstrate how these changes in the cavity system could be driven by the pressure fluctuations predicted within the channelised drainage system. This enables a system scale model of glacier hydrology to be developed, which is presented in the final chapter, linking variations in surface melt rate to channel pressure, cavity volume and ultimately ice motion. In summary, this research has helped to illuminate the morphology and functioning of the drainage system of Leverett Glacier. This has improved our understanding of how hydrology influences both the motion of the Greenland Ice Sheet and its impact on the underlying topography, and enabled better prediction of how these processes are influenced by changes in climate.