Abstract: Gauge theories are at the heart of our modern understanding of physics, but solving their out-of-equilibrium dynamics is extremely challenging for classical computers. This difficulty is currently spurring a worldwide effort to solve gauge theories on dedicated quantum computing devices. In this talk, I will discuss recent progress towards quantum simulation of gauge theories, especially focusing on ultracold atoms. I will present a recent breakthrough experiment that has realized a many-body gauge theory in a 71-site Hubbard model and has certified the fulfilment of Gauss’s law for the first time. Moreover, I will discuss our ongoing theoretical effort to quantify and mitigate the influence of microscopic violations of the local gauge symmetry. Through these discussions, I will aim at outlining a roadmap towards mature and practically relevant quantum simulation of gauge theories.