Recent observations of the high-redshift universe have characterized the initial conditions for nonlinear structure formation over the full range of scales responsible for dwarf and giant galaxies, galaxy clusters and the large-scale cosmic web. At the same time, wide-field spectroscopic and photometric surveys have measured the abundance and clustering of low-redshift galaxies as a function of mass, size, morphology, kinematic structure, gas content, metallicity, star formation rate and nuclear activity, while deep surveys have explored the evolution of several of these distributions to z > 3. Galaxy population simulations aim to interpret these observations within the Lambda Cold Dark Matter (LCDM) structure formation paradigm, thereby constraining the complex, diverse and heavily interconnected astrophysics of galaxy formation. Recent simulations are broadly consistent with the galaxy abundances and clustering seen in both wide-field and deep surveys, and provide predictions for topics as different as galaxy-galaxy lensing, the triggering and duty cycles of AGN, and the evolution of Tully-Fisher, mass-size and mass-metallicity relations. They show galaxy assembly histories to be strongly constrained by the structure formation paradigm, giving insight into issues such as internally versus externally driven evolution, inflow versus winds, major versus minor mergers, in situ versus ex situ star formation, and disks versus bulges. In addition, simulations can now be adapted to represent any chosen LCDM-like cosmology, allowing a first assessment of whether galaxy formation uncertainties will limit our ability to do precision cosmology with galaxy surveys.