Recent advances in artificial intelligence and robotics promise a future in which autonomous systems will help with societally beneficial tasks that are dangerous, tedious or too costly for humans. In this talk, I will give examples of such tasks, and explain why delivering them requires autonomous systems that can operate resiliently in the presence of high levels of uncertainty and disruption. I will then argue that the development and operation of resilient autonomous systems pose unprecedented and complex sociotechnical challenges. For some of these challenges, I will present possible preliminary solutions. For others, I will only be able to suggest open research questions that must be addressed before progress can be made.