The Antarctic grounding zone has a disproportionately large effect on glacier dynamics and ice sheet stability relative to its size but remains poorly characterised across much of the continent. Accurate ice velocity and thickness information is needed in the grounding zone to determine glacier outflow and establish to what extent changing ocean and atmospheric conditions are affecting the mass balance of individual glacier catchments. This thesis describes new satellite remote sensing techniques for measuring ice velocity and ice thickness, validated using ground measurements collected on the Beardmore, Skelton and Darwin Glaciers and applied to other Transantarctic Mountain outlet glaciers to determine ice discharge. Outlet glaciers in the Transantarctic Mountains provide an important link between the East and West Antarctic Ice Sheets but remain inadequately studied. While long-term velocities in this region are shown here to be stable, instantaneous velocities are sensitive to stresses induced by ocean tides, with fluctuations of up to 50% of the mean observed in GPS measurements. The potential error induced in averaged satellite velocity measurements due to these effects is shown to be resolvable above background noise in the grounding zone but to decrease rapidly upstream. Using a new inverse finite-element modelling approach based on regularization of the elastic-plate bending equations, tidal flexure information from differential InSAR is used to calculate ice stiffness and infer thickness in the grounding zone. This technique is shown to be successful at reproducing the thickness distribution for the Beardmore Glacier, eliminating current issues in the calculation of thickness from freeboard close to the grounding line where ice is not in hydrostatic equilibrium. Modelled thickness agrees to within 10% of ground penetrating radar measurements. Calibrated freeboard measurements and tide-free velocities in the grounding zones of glaciers in the western Ross Sea are used to calculate grounding zone basal melt rates, with values between 1.4 and 11.8 m/a⁻¹ in this region. While strongly dependent on grounding line ice thickness and velocity, melt rates show no latitudinal trend between glaciers, although detailed error analysis highlights the need for much improved estimates of firn density distribution in regions of variable accumulation such as the Transantarctic Mountains.