Cosmological simulations are among the most powerful tools available to probe the non-linear regime of cosmic structure formation. They also provide a clear test-bed for understanding the impact that hydrodynamics and feedback processes have on the evolution of galaxies. I will present an overview of modern galaxy formation simulations that couple a novel moving mesh computational method with explicit baryon feedback prescriptions. This approach results in detailed galaxy formation models that reproduce fundamental observations such as the galaxy stellar mass function, cosmic star formation rate density, and galaxy morphological diversity. In turn, we are able to leverage these simulations to derive physical knowledge on a wide range of science questions, including the importance of supernova and black hole feedback on galaxy growth, the impact of environment on galaxy properties, the origin of diverse morphological types, and much more. I will discuss ongoing efforts to improve the physical fidelity of our simulations, which will continue to play an increasingly large role in building a comprehensive theory for galaxy formation over the coming decades.