  The formation of stars from gas drives the evolution of galaxies. Yet, it
remains one of the hardest processes to understand when trying to connect
observations of stellar and galaxy populations to models of large scale
structure formation. The star formation rate at redshifts z > 2 drops off
rather more quickly than was thought even five years ago. Theoretical models
have tended to overpredict the star formation rate at these high redshifts
substantially, primarily due to overcooling. Overcooling in galaxies typically
occurs because of unphysical radiative cooling. As a result, insufficient
turbulence is driven by stellar feedback. I show that such turbulence has the
net effect of strongly inhibiting star formation, despite its ability to
locally promote star formation by compression. Radiation pressure appears less
likely to be a dominant driver of the turbulence than has been argued, but
supernova and magnetorotational instabilities remain viable. Gravity alone
cannot be the main driver, as otherwise well-resolved models without feedback
would accurately predict star formation rates. Star formation rate surface
density correlates well with observed molecular gas surface density, as well as
with other tracers of high density material. Correlation does not, however,
imply causation. It appears that both molecule formation and star formation
occur as a consequence of gravitational collapse, with molecules not essential
in cooling. The basic concept that gravitational instability drives star
formation remains a true guide through the thickets of complexity surrounding
this topic. I finally briefly note that understanding ionization heating and
radiation pressure from the most massive stars will likely require much higher
resolution models (sub-parsec scale) than resolving supernova feedback.
(lightly abridged)
