I will describe the numerical efforts to simulate galaxies with the code AREPO across an unprecedented range of halo masses, environments, evolutionary stages and cosmic times. In particular, I will present an overview of the IllustrisTNG project, a collaboration among Heidelberg, Munich, New York and Boston. There we are simulating a series of three cosmological volumes (50, 100, 300 Mpc a side, respectively) capable of both resolving the inner structures of galaxies as small as the classical dwarfs of the Milky Way, as well as of sampling the large scale structure of the Universe with thousands among groups and clusters of galaxies. I will briefly review what is explicitly and empirically solved in gravity+magnetohydrodynamics simulations for galaxy formation in a cosmological context and what is required and what it means to “successfully” reproduce populations of galaxies which resemble the real ones. I will therefore show preliminary applications from the IllustrisTNG simulations. These may include our theoretical expectations for the distribution of dark matter on large scales and within galaxies, the build up and characterisation of the faint stellar envelopes around galaxies and their connections to their host haloes, the emergence of the galaxy colour bimodality, and the modes of galaxy quenching in diverse environments.