Even with government pledges to reduce greenhouse gas emissions as part of the Paris Agreement, we are likely committed to 3-4C surface warming above pre-industrial levels by 2100 CE, leading to enhanced ice-sheet melt. But the mechanisms by which the Greenland and Antarctic ice sheets advance and retreat differ, so it isn't always clear how sensitive each might be to future warming amounts or to the predicted rates. In this presentation I will describe the underlying mechanisms that control ice sheet dynamics, and will use examples spanning the past, present, and future to illustrate the degree to which these systems are understood, and where the key uncertainties remain. I will explore some of the ways in which geological data are used to constrain model parameterisation (or not), and how a combined empirical-numerical approach can lead to useful advances. Finally, I will demonstrate how satellite-based measurements of recent ice mass change can be employed to constrain Greenland and Antarctic ice-sheet simulations, allowing future melting to be accurately modelled. We will look at how this simulated melt will impact the global climate, for example, by slowing the Atlantic overturning circulation or trapping warm water below the sea surface around Antarctica, creating a positive feedback that accelerates ice-sheet retreat. Our latest results suggest that over the next century Greenland will contribute linearly to sea-level rise under a warming climate, whereas the response from Antarctica may only emerge after 2070, once dynamic thinning outweighs increased snowfall. When we then use a self-consistent sea-level model to predict the redistribution of this water, we see that island nations in the central Pacific will probably experience the greatest sea-level rise - yet perhaps have the least socio-economic capacity to adapt.