The world’s deltas are facing a sustainability crisis, with many at high risk of being ‘drowned’ as a result of relative sea-level rise. The only factor that can potentially offset relative sea-level rise is the deposition of fluvial sediment on the surface of deltas. As a result, an understanding of trends in fluvial sediment supply to deltas is critical for understanding the potential of different deltas to adapt to the threat of drowning. Here trends of sediment supply to three of the world’s deltas (the Ganges-Brahmaputra, Mahanadi and Volta) are considered and the prospects for the future of these and other deltas discussed, focusing on how human activity can be modified to promote a more sustainable future for at-risk deltas.