I will present efforts to understand this behaviour using mathematical models. I will discuss the current hypotheses for what is happening to the drainage system beneath the ice. In the simplest description, water flows through a sequence of connected cavities formed as the ice slides over small-scale bumps in the bed. The water flow generates heat, melting the ice and causing the formation of river-like channels. This evolution of the drainage system significantly alters its capacity to drain the water from the crevasses, and ultimately controls the rate at which the ice slides. I will show calculations of ice flow for different amounts of melting to investigate the impact of recent climatic changes on the Greenland Ice Sheet.