Anthropogenic emissions of greenhouse gases are warming the Earth. It is likely that the greatest impacts of climate change on human and natural systems will come from increasingly frequent and severe extreme weather and climate events. Some increases in such extremes are already being detected, and this trend is projected to continue as Earth warms. Here we review the overarching climate drivers of increases in extreme weather and address the context in which extremes occur and the challenges of projecting future changes. The observational evidence for climate-driven increases in extremes and the implications of model projections are reviewed for heat and drought and several types of storms: tropical cyclones, midlatitude storms, and severe local weather, focusing on those changes most relevant to the continental United States. We emphasize the overall observed and modeled trends in extreme weather in which we have the greatest confidence, because they are consistent with our fundamental understanding of weather and climate. Despite remaining uncertainty about many details, especially in model-based projections, the signal of increasing extremes is sufficiently clear that it demands a robust human response, in limiting future emissions of greenhouse gases and in making our human systems more resilient to further changes that are inevitable as Earth continues to warm.Implications: By placing observed and projected changes in extreme weather in the context of our fundamental understanding of physics and statistics, this review makes it clear that these are significant and impactful changes that demand a robust human response.