  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.
