This thesis details the application of numerical modelling techniques to simulate erosion under ice sheets with the aim of better understanding the interrelationships between glacial erosion, long-term landscape evolution and ice dynamics. A model is developed that predicts patterns of basal erosion in a glaciologically sensible manner and shows that 'fluvial' landscapes can become 'glacial' systems within 100 kyrs. By simulating ice sheet growth and erosion over synthetic landscapes of varying form, amplitude and wavelength the topographic characteristics that are most critical to the evolution of ice dynamics, and to ongoing erosion are identified. The model is applied to the solution of two puzzles regarding the interaction of ice, erosion and landscape in Patagonia and Antarctica. In settings similar to Patagonia, glacial erosion is shown to be able to drive large-scale change in ice dynamics on 10⁵ to 10⁶ year timescales. This goes some way to explaining the behaviour of the Patagonian ice sheet since the 'Greatest Patagonian Glaciation', whereby ice extents reduce over successive glacial cycles, contradicting patterns of global ice volume. In Antarctica, the model is used to predict the pattern of long-term ice mass expansion and associated patterns of landscape evolution. For the first time, predictions tied to ice dynamics are made regarding the degree to which the Antarctic landscape has been modified by ice as it expands from local to regional ice centres and then to a continental scale ice sheet. Common themes throughout this thesis are that preglacial landscape geometry is a critical driver of the pattern of landscape evolution under ice, and that erosion should no longer be considered a passive component of any glacial system over timescales of 10⁵ and greater.