The majority of the ice flowing from the Antarctic interior makes its way to the ocean through fast-flowing ice streams, or glaciers. Understanding what controls the speed of these streams is extremely important in predicting the overall response of ice sheets to changing climatic conditions, and hence in predicting future sea-level rise. A major factor determining the flux of grounded ice towards the ocean is the rate at which the ice slides over its bed, which is sensitive to conditions at the base of the ice such as shear stress and water pressure, and the material making up the bed. However, it remains difficult to measure and predict the evolution of these variables over the scale of ice sheets, and to accurately model their effect on sliding speed. In this thesis, I present novel methods to constrain and model the basal dynamics of ice, particularly motivated by observations of tidally-driven acceleration of Antarctic glaciers. In the first chapter, I review recent observations of spatial and temporal variability in ice velocity, existing simplified models of the flow of Antarctic ice streams, and sources of uncertainty in projections of ice-sheet mass loss. In the next section of the thesis I explore the link between ocean forcing and the water pressure beneath the grounded ice, by considering subglacial water transport at a tidally migrating grounding line. In chapter 2, I develop a model for the retention of water in the subglacial environment during the receding tide. This problem constitutes an elastic analogue to the Landau-Levich problem, where the thickness of the deposited fluid layer depends on the elasticity of the overlying sheet. I contrast the slow dynamics of the outgoing tide with the relatively fast dynamics of water entering the subglacial cavity during the incoming tide in chapter 3. This results in a non-linear filter between the ocean tides and the water pressure below the upstream ice sheet. In chapter 4, I develop a model for the deformation of subglacial sediment subject to these periodic pressure fluctuations, and investigate how the transient sliding speed can deviate from the steady dynamics. Using a water-saturated granular rheological model for the sediment, I derive time-dependent traction laws linking basal drag, sliding speed, water pressure and till flux. I apply this granular model as a boundary condition on ice flow through an idealised ice stream in chapter 5, and calculate the surface velocity response. In chapter 6, I return to grounding-line processes, where I link grounding-line migration and sediment redistribution to the formation of tidally-modulated bedforms. The observation and modelling of these bedforms provides constraints on both the rheology of subglacial sediments and the retreat rate of paleolithic ice sheets. Finally in chapter 7, I conclude and discuss future directions of this work.