Ongoing sea-level rise has brought renewed focus on terrestrial sediment supply to the coast because of its strong influence on whether and how long beaches, marshes and other coastal landforms may persist into the future. Here, we summarise findings of sediment discharge from several coastal rivers, revealing that infrequent, large-magnitude events have disproportionate influence on the morphodynamics of coastal landforms and littoral cells. These event-dominated effects are most pronounced for small, steep mountainous rivers that supply beach and wetland sediment along the world’s active tectonic margins, although infrequent events are important drivers of sediment discharge for rivers worldwide. Additionally, extreme events (recurrence intervals of decades to centuries) that follow wildfires, earthquakes, volcanic eruptions, extreme precipitation or – most notably – combinations of these factors can redefine coastal sediment budgets and morphology. Some of these extreme events (e.g., wildfires plus rainfall) are increasing in magnitude and frequency under modern climate warming, with the likely result of increasing sediment flux to affected coastlines. Climate change is also altering watershed processes in both high latitudes and high altitudes, resulting in increased sediment supply to downstream catchments. We conclude that sediment inputs to coastal systems are highly variable with time, and that the variability and trends in sediment input are as important to characterise as long-term averages.