This paper provides a systematic review of the literature on 80 experimental, hypothetical survey and market data studies of insurance demand against low‐probability/high‐impact risks. The objective of the review is to extract lessons from these studies and to outline an agenda for future research. We contrast the results of experimental and survey studies to findings from market data. We focus on experimental design methods, insurance characteristics, as well as results about theories, heuristics, behavioural biases and explanatory variables. Lessons for policymakers are drawn which can facilitate disaster preparedness.