"The Illustris simulation: novel successes and remaining challenges in hydrodynamical modelling of galaxy formation": I will present first results from the Illustris simulation, which is a cosmological hydrodynamical simulation using 2*1820^3 resolution elements. The simulation follows thousands of massive galaxies down to z=0 inside a (100Mpc)^3 volume, resolving <~kpc scales. It is run using the Arepo moving-mesh code to model gravity and hydrodynamics, as well as cooling, stellar population evolution, and various feedback processes. I will discuss a broad range of observables at z=0->5 that Illustris matches reasonably well (and not particularly tuned for), including galaxy masses, morphologies, and spatial distributions. I will also present points of failure that can guide us how to further improve our models.