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We survey the growing literature on fat-tailed distributions in environmental economics. We then examine the theoretical and statistical properties of such distributions, focusing especially on when these properties are likely to arise in environmental problems. We find that a number of variables are fat tailed in environmental economics, including the climate sensitivity, natural disaster impacts, spread of infectious diseases, and stated willingness to pay. We argue that different fat-tailed distributions arise from common pathways. Finally, we review the literature on the policy implications of fat-tailed distributions and controversies over their interpretation. We conclude that the literature has made great strides in demonstrating when fat tails matter for optimal environmental policy. Yet, much is less well understood, including how alternative policies affect fat-tailed distributions, the optimal policy in a computational economy with many fat-tailed problems, and how to account for imprecision in empirical tests for fat tails. Expected final online publication date for the Annual Review of Resource Economics, Volume 13 is October 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.