Climate change has increased the frequency and intensity of natural disasters. Does this translate into increased economic damages? To date, empirical assessments of damage trends have been inconclusive. Our study demonstrates a temporal increase in extreme damages, after controlling for a number of factors. We analyze event-level data using quantile regressions to capture patterns in the damage distribution (not just its mean) and find strong evidence of progressive rightward skewing and tail-fattening over time. While the effect of time on averages is hard to detect, effects on extreme damages are large, statistically significant, and growing with increasing percentiles. Our results are consistent with an upwardly curved, convex damage fu...