Events with very low a-priori probability but very high impact shape our lives to a significant degree, on an individual as well as a global level. Unfortunately, people have difficulties understanding and processing the prospects of such events, leading to idiosyncratic behavior. In this article I summarize the main findings regarding human behavior in the context of low-probability high-impact events and identify the main sources of bias and other idiosyncrasies, specifically: [1] ignorance of critical events due to biased information search, [2] a false sense of security due to reinforcement learning and reliance on small samples, [3] biased evaluation of likelihood due to mental availability and affective content, and [4] inaccurate interpretation of risks due to the format by which they are communicated. I further suggest ways to mitigate these problems and areas where additional research is needed. Lastly, I emphasize that, in order to create useful interventions, more research on the interplay and the dynamics of effects, as well as more research based on practical rather than laboratory contexts, is needed.