Statistical distributions of flood peak discharge often show heavy tail behavior, that is, extreme floods are more likely to occur than would be predicted by commonly used distributions that have exponential asymptotic behavior. This heavy tail behavior may surprise flood managers and citizens, as human intuition tends to expect light tail behavior, and the heaviness of the tails is very difficult to predict, which may lead to unnecessarily high flood damage. Despite its high importance, the literature on the heavy tail behavior of flood distributions is rather fragmented. In this review, we provide a coherent overview of the processes causing heavy flood tails and the implications for science and practice. Specifically, we propose nine hypotheses on the mechanisms causing heavy tails in flood peak distributions related to processes in the atmosphere, the catchment, and the river system. We then discuss to which extent the current knowledge supports or contradicts these hypotheses. We also discuss the statistical conditions for the emergence of heavy tail behavior based on derived distribution theory and relate them to the hypotheses and flood generation mechanisms. We review the degree to which the heaviness of the tails can be predicted from process knowledge and data. Finally, we recommend further research toward testing the hypotheses and improving the prediction of heavy tails. Plain Language Summary Statistical distributions are used to estimate the probability of flood peaks, which in turn is needed for risk management and the design of flood protection. Flood peak distributions often show heavy tail behavior, that is, extreme floods are more likely to occur than would be predicted by commonly used distributions that have exponential asymptotic (light tailed behavior). This heavy tail behavior may surprise flood managers and citizens, as human intuition tends to expect light tail behavior. In this review, we summarize the knowledge about the causes of heavy flood tails. To this end, we discuss the flood generation processes in the atmosphere, catchment, and river system, that tend to generate heavy‐tailed flood peak distributions. Key Points Heavy tail behavior of flood peak distributions may lead to surprise and high flood damage We propose nine hypotheses on the mechanisms causing heavy tails in flood peak distributions We review to which extent the current knowledge supports or contradicts these hypotheses