Abstract: Horizon-scale observations of accreting supermassive black holes with the Event Horizon Telescope (EHT) have opened a new window onto strong-field gravity and black-hole accretion. The EHT's 2022 observations of Sagittarius A* (Sgr A*), the black hole at the center of our Galaxy, provide a new opportunity to test the Kerr metric in a previously unexplored regime. I will discuss the EHT observations of Sgr A*, focusing on what they can reveal about fundamental physics, and briefly compare these results with the earlier observations of M87*. I will then discuss how improvements in both observations and data analysis can extend these measurements in the near future. In particular, I will introduce PRIMO, a machine-learning algorithm for EHT data analysis that uses a large library of high-fidelity simulations as a training set. I will show a higher-resolution reconstruction of M87* obtained with PRIMO and demonstrate how improved image reconstruction can provide new constraints on both black-hole accretion and strong-field gravity.
