This report summarizes current research on how climate change is likely to influence future losses from extreme weather events. We consider six types of weather-related extreme events: tropical cyclones, extratropical cyclones, inland floods, landslides and avalanches, wildfires, and small-scale storms. For each type of event, we synthesize existing research related to three topics. First, we examine research that estimates historical average losses from each type of extreme weather. We find that while there are relatively good data on costs of destroyed infrastructure, there is considerable disagreement in the literature about the longer-term macroeconomic effects of disasters. Second, we summarize evidence on the relationship between socioeconomic growth and storm losses. Our review suggests that increases in GDP and population lead to higher losses from disasters, but that disaster mortality is lower in more developed countries. Finally, we review studies of how climate change will affect future losses from extreme weather. Many studies predict increases in losses under climate change, but the science remains uncertain and some projections suggest that certain types of extreme weather losses may decrease. Overall, based on a reduced-form model that draws together parameter estimates from each of these three strands of literature, we estimate that moderate climate change will cause average extreme weather damages to increase by tens of billions of dollars per year. However, the confidence intervals surrounding our estimates are very wide, reflecting substantial underlying uncertainties.