I will describe what Google's 2019 quantum supremacy experiment  was, how their quantum computer works, and address some of the controversy around the results. Caveat: I am in no way affiliated with Google.
Google's quantum computing group, headed by John Martinis at UCSB, built a quantum computer that completed a computational task many orders of magnitude faster (200 sec) than any conventional computer could (10000 years), and this advantage is scalable. Their quantum computer (codename: Sycamore) has 53 qubits, consists of superconducting circuits built with integrated-circuit technology. The task was sampling from a special, practically uncomputable random sequence, corresponding to the output of a noisy random quantum circuit. I will discuss in detail why this specific task was chosen, what statistics tools were used to demonstrate supremacy. I will also address some of the criticism about the experiment, coming from IBM, Gil Kalai, and others.
: Quantum Supremacy using a programmable superconducting processor, Arute et al, Nature 574, 505 (2019)