Contemporary cosmological hydrodynamical simulations are reaching unprecedented levels of sophistication and complexity. Numerical programs like IllustrisTNG (www.tng-project.org) are allowing us to model reasonably realistic populations of galaxies across an ever-wider range of masses, environments, evolutionary stages and cosmic epochs. There we resolve and model the structural details of thousands of galaxies together with the large-scale cosmic web by solving the equations of gravity and magnetohydrodynamics and by including prescriptions for star formation, stellar evolution, metal enrichment, cooling and heating of the gas, galactic outflows and feedback from the supermassive black holes, all within the boundary conditions of our standard cosmological paradigm. In this talk, I will give an overview of our efforts to generate and effectively exploit these types of models and I will showcase some of the astrophysical insights that they are allowing us to uncover and quantify. Finally, I will show how the combination of Deep Learning methods and large-volume galaxy simulations allows us to infer unobservable quantities, such as information about the past assembly and merger history of galaxies, from their observable properties.”