I will present hydrodynamical simulations of the formation of dwarf galaxies starting from cosmological initial conditions at high redshift. In these simulations, a novel numerical implementation of stellar feedback resulting from momentum imparted to the ISM by radiation, supernovae, and stellar winds has been used (Hopkins et al. 2011). Our final objects have structure and stellar populations consistent with observed dwarf galaxies. First results indicate that feedback from massive stars plays a critical role in shaping the galaxy mass function, the structure of the interstellar medium (ISM), and the low efficiency of star formation.