AbstractThe 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 modern and high-redshift stellar and galaxy populations to models of large scale structure formation. It has become clear that 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 in galaxies. 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 mechanisms. 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, necessarily imply causation. In this case, it appears that both molecule formation and star formation occur as a consequence of gravitational collapse, with molecules typically playing an important but not an essential role 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.