Rising global sea level, a consequence of climate change, results from an increase in the world ocean’s water volume and mass. Recent climate warming is responsible for producing the highest rate of global average sea-level rise of the past few millennia, and this rate will accelerate through the 21st century and beyond, exposing low-lying islands and coastal regions to significant flood risks. The flood risks can be compounded or diminished locally because changes in sea level are not uniform. In this review, we briefly discuss ice sheets as drivers of global and local sea levels, and how they could evolve under modern climate change. We underline some of the impacts of sea level change on coastal communities, and emphasize that local sea-level projections can be very different from estimates of the global average.