Climate change poses significant risks around the world. Rising global sea levels are among the most salient hazards caused by global warming, as nearly 900 million people globally live in exposed coastal areas. This exposure necessitates the development of coastal risk management strategies. The efficacy of such strategies relies on sound projections of future global climate, including sea levels. However, a variety of threshold responses challenge attempts to generate harmonized estimates of future sea levels, including potentially sizable contributions from the Antarctic and Greenland ice sheets. Here, we assemble current research on global sea-level change and efforts to better understand its uncertainties and their impacts. We review the varying geophysical factors that contribute to changes in global mean sea level, as well as how these assessments of sea level can be brought to bear on local flood risk analyses. We discuss the major sources of uncertainty facing projections of global sea level, including both shallow and deep uncertainties. Finally, we identify current gaps and opportunities for the research community to better meet the needs of decision-makers to manage the risks posed by sea-level rise in the twenty-first century and beyond.