In this talk, I will describe ongoing work to study galaxy formation and evolution in a cosmological framework with numerical simulations. The simulations are performed using a moving-mesh approach that inherits advantages of traditional particle- and grid-based methods by combining continuous spatial and temporal adaptivity with accurate solutions to the fluid equations of motion. Physically motivated models are included in the simulations to account for feedback from stellar evolution and black hole growth, processes thought to be essential to galaxy assembly. Some applications of the simulations will be presented, including galaxy morphologies and fine structure; tracking galaxies in time; stellar halos and their age and metallicity gradients; and the merger rate of galaxies. Shortcomings of the simulations will be discussed along with efforts to refine the modelling to give better agreement with certain observables.