What Have Google's Random Quantum Circuit Simulation Experiments Demonstrated about Quantum Supremacy?

Quantum computing is of high interest because it promises to perform at least some kinds of computations much faster than classical computers. Arute et al. 2019 (informally, "the Google Quantum Team") report the results of experiments that purport to demonstrate "quantum supremacy" -- the claim that the performance of some quantum computers is better than that of classical computers on some problems. Do these results close the debate over quantum supremacy? We argue that they do not. We provide an overview of the Google Quantum Team's experiments, then identify some open questions in the quest to demonstrate quantum supremacy.