Recent progress in simulating galaxy formation from the largest to the smallest scales

Galaxy formation simulations are an essential part of the modern toolkit of astrophysicists and cosmologists alike. Astrophysicists use the simulations to study the emergence of galaxy populations from the Big Bang, as well as the formation of stars and supermassive black holes. For cosmologists, galaxy formation simulations are needed to understand how baryonic processes affect measurements of dark matter and dark energy. Owing to the extreme dynamic range of galaxy formation, advances are driven by novel approaches using simulations with different tradeoffs between volume and resolution. Large-volume but low-resolution simulations provide the best statistics, while higher-resolution simulations of smaller cosmic volumes can be evolved with self-consistent physics and reveal important emergent phenomena. I summarize recent progress in galaxy formation simulations, including major developments in the past five years, and highlight some key areas likely to drive further advances over the next decade.