We present an overview of some of the issues surrounding current models of galaxy formation, highlighting recent insights obtained from cosmological hydrodynamic simulations. Detailed examination of gas accretion processes show a hot mode of gas cooling from near the halo's virial temperature, and a previously underappreciated cold mode where gas flows in along filaments on dynamical timescales, emitting its energy in line radiation. Cold mode dominates in systems with halo masses slightly smaller than the Milky Way and below, and hence dominates the global accretion during the heydey of galaxy formation. This rapid accretion path enables prompt assembly of massive galaxies in the early universe, and results in $z\sim 4$ galaxy properties in broad agreement with observations, with the most massive galaxies being the most rapid star formers. Massive galaxies today are forming stars at a much reduced rate, a trend called downsizing. The trend of downsizing is naturally reproduced in simulations, owing to a transition from cold mode accretion in the early growth phase to slower hot mode accretion once their halos grow large. However, massive galaxies at the present epoch are still observed to have considerably redder colors than simulations suggest, suggesting that star formation is not sufficiently truncated in models by the transition to hot mode, and that another process not included in current simulations is required to suppress star formation.

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