Galaxy formation is a complicated process that is notoriously hard to model due to both the large variety of physical phenomena that are involved and the huge dynamic range that they encompass. I will present recent results from the Illustris project, which is a set of cosmological hydrodynamical simulations run to z=0, including the largest ever performed. The simulations are run with the moving-mesh code Arepo, and include physical processes critical for galaxy formation. In many respects, the Illustris galaxy populations resemble the galaxy populations observed in the real Universe. I will discuss various aspects of the galaxy formation process as it appears in these simulations.