From time to time, something occurs which is outside the range of normal expectations. We will call these “tail events” in the sense that they are way out of the tail of a probability distribution. I consider the question of the implications of tail events for economic policy and climate-change economics. This issue has been analyzed by Martin Weitzman who proposed a Dismal Theorem. The general idea is that, under limited conditions concerning the structure of uncertainty and risk aversion, society has an indefinitely large expected loss from high-consequence, low-probability events. Under such conditions, standard economic tools such as cost-benefit analysis cannot be applied. The present study is intended to put the Dismal Theorem in context and examine the range of its relevance, with an application to catastrophic climate change. I conclude that tail events are sometimes of extreme importance, and we must be extremely careful to include them in situations of deep uncertainty. However, we conclude that no loaded gun of strong tail dominance has been uncovered to date.