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Within the past two years, groups at Google and USTC China made the first serious claims of "quantum supremacy": that is, the use of quantum computers to solve certain contrived sampling problems faster than any existing classical computer using any currently-known method. These experiments built on theoretical work that I and others did over the last decade. In this talk, I'll try to start with these experiments -- what exactly was done, the criticisms raised against these experiments and against the whole concept of quantum supremacy, the responses to some of the criticisms -- and then work forward, to the fraught, hype-filled landscape of (alleged) near-term applications of noisy quantum computers, the eventual applications of full fault-tolerant quantum computers, and finally what quantum computing means for our understanding of the world.