The recent demonstration of quantum supremacy by Google is a first step towards the era of small to medium scale quantum computers. In this talk I will explain what the experiment accomplished and the theoretical work it is based on, as well as what it did not accomplish and the many theoretical and practical challenges that remain. I will also describe recent breakthroughs in the design of protocols for the testing and benchmarking of quantum computers, a task that has deep computational and philosophical implications. Specifically, this leads to protocols for scalable and verifiable quantum supremacy, certifiable quantum random generation and verification of quantum computation.