Sea-level rise as a consequence of climate change will have severe impacts on coastal populations and ecosystems. However, owing to the incomplete state of scientific knowledge, there is a large range of uncertainty in the predictions, of a factor of more than two for any given emissions scenario during the 21st century, and much larger for subsequent centuries. This is a serious obstacle to the assessment of impacts. Sea-level change is a diagnostic of a complex combination of Earth system processes operating over a wide range of timescales. Explaining the record of past sea-level change and predicting the future is therefore a fascinating interdisciplinary scientific challenge as well as one with practical implications. The aim of this project is to improve quantitative understanding and hence reduce uncertainty in predictive models of the two main climate-related contributions to sea-level change, namely ocean density change and changes in ice-sheets. The former is the most important term on timescales of years to centuries, and the latter is the principal influence over timescales of centuries to millennia. In both parts of the proposal, our focus is on analysis of changes simulated by 3D atmosphere-ocean climate models, which we compare with observational data. For ocean density change, the objectives are to analyse the physical processes responsible for global-mean and local sea-level change due to density change, in order to quantify and constrain the uncertainties in predictions. For ice-sheets, the objectives are to increase our understanding of and ability to model the coupled evolution of ice-sheets and climate on multi-millennial timescales, in particular regarding the last glacial cycle and the long-term future of the Greenland ice-sheet.