Abstract: I investigate three related questions in the theory of star formation. First, I consider the physical mechanism of massive star formation. Massive stars reach the main sequence while still accreting from their natal clouds, leading to a huge radiation pressure force on dust grains suspended in the incoming gas. Early calculations found that this limits stellar masses to $\lesssim$20--40 $M\odot$, far smaller than the most massive stars observed. I demonstrate two new mechanisms by which accretion can continue despite radiation pressure. First, radiation holding up a massive infalling envelope is subject to Rayleigh-Taylor instability, which forces the accreting gas into optically thick filaments that are shielded from radiation and channel gas to the star. Second, massive protostars have powerful outflows that punch optically thin cavities through the envelope. These channel radiation away from the accreting gas, greatly reducing the radiation pressure force it experiences. Second, I argue that the stellar initial mass function (IMF) does not originate from the 'competitive accretion' of unbound gas by seed protostars. I provide an approximate solution to the problem of Bondi-Hoyle accretion in a turbulent medium, and use this solution to show that the rate of competitive accretion in environments like observed star-forming regions is too low to substantially affect the masses of newborn stars. Only if star-forming clumps undergo a global collapse to a state far denser than any thus far observed is competitive accretion a viable mechanism for producing the IMF. Third, I give a theoretical prediction for the star formation rate in a medium where star formation is regulated by supersonic turbulence. Starting from the approximation that stars form in any region that is sufficiently overdense for the local potential energy to exceed the turbulent kinetic energy, I derive a formula for the star formation rate in terms of the virial parameter and Mach number of a star-forming cloud. I show that this prediction is consistent with simulations, that it correctly predicts the observed star formation rate in the Milky Way, and that it reproduces the observed Kennicutt-Schmidt Law for star formation in galaxies.