Sea level rise is one of the greatest climate change risks to society and the environment. The contribution of the Antarctic Ice Sheet to future sea level rise is receiving a lot of attention due to uncertainties in the magnitude and timing of its response to climate forcing. Here, I give an overview of some recent contributions to reducing uncertainties in ice sheet model simulations of: (1) the processes governing Antarctic ice flow; and (2) the response of the ice sheet to ocean forcing. The first part of my talk will focus on recent advances in modeling internal deformation, a key driver of polar ice sheet flow whose contribution to the stability and evolution of the Antarctic Ice Sheet is often overlooked in contrast with basal sliding. I contrast model simulations of ice sheet dynamics using the Glen flow relation and the ESTAR flow relation - a new description of internal deformation that takes into account the impact of different types of stresses on the overall flow regime. The two flow relations simulate markedly different flow regimes: over the Thwaites Glacier, the Glen flow relation underestimates the contribution of internal deformation to overall flow by up to a factor of three. Compared with the ESTAR flow relation, the Glen flow relation simulates unrealistically fast thinning ice near the calving front of an idealised ice shelf, leading to unrealistic ice shelf geometries. Given that internal deformation is the main driver of ice shelf flow, this result could have a significant impact on buttressing, and has important implications for ice sheet models used to constrain uncertainty in reconstructions and projections of sea levels. The second part of my talk focuses on current research investigating the impact of internal variability in ocean melt rates on ice sheet dynamic flow. I use output from a Regional Ocean Model System simulation of the Sabrina Coast sector to inform forcing time series of ocean melt rate variability, applying these to an ice sheet model of the Totten Glacier, East Antarctica. The Totten Glacier grounding line is found to be highly sensitive to small variations in the magnitude of the background ocean temperature forcing. Even in the absence of climate change forcing, ocean melt rate variability on interannual time scales (2-7 years) is sufficient to generate grounding line migration of a similar magnitude to observed. These results highlight the need to account for internal ocean variability in projections of future sea level rise from the Antarctic Ice Sheet.