Achieving the human-level safety performance for autonomous vehicles (AVs) remains a challenge. One critical bottleneck is the so-called “long-tail challenge”, which usually refers to the problem that AVs should be able to handle seemingly endless low-probability safety-critical driving scenarios, even though millions of testing miles have been accumulated on public roads. However, there is neither rigorous definition nor analysis of properties of such problems, which hinders the progress of addressing them. In this talk, ww reveal that the rarity of safety-critical events in high-dimensional driving environments is the root cause of the “long-tail challenge”. We formulate it as “curse of rarity” (CoR) because it occurs ubiquitously in various safety-critical systems such as medical diagnosis and aerospace systems. We hope to provide a better understanding of the safety challenges faced by the AV community, therefore accelerate the development and deployment of AVs.