The formation of massive stars remains one of the most significant unsolved problems in astrophysics, with implications for the production of heavy elements in the universe and the structure and evolution of galaxies. High mass star formation poses a major theoretical challenge:
How is it possible to sustain a sufficiently high mass accretion rate into a protostellar core despite the radiation pressure and the dynamical effects of protostellar outflows on the accreting envelope. I present a series of our recent high resolution radiation-hydrodynamic adaptive mesh refinement simulations including for the first time the feedback effects of protostellar outflows on the formation of massive stars by comparing the effects of protostellar outflow feedback with our earlier work that did not include outflows. I show that feedback from protostellar outflows creates highly evacuated optically thin cavities in the surrounding core, drives Kelvin Helmholtz instabilities in the core and allows the efficient escape of radiation through the development of an anisotropic radiation field. I show that with the additional mechanism of protostellar outflows, radiation pressure again cannot halt accretion thereby allowing massive stars to form. I present predictions for massive star formation including outflows with upcoming ALMA submillimeter observations. Finally, with high resolution radiation-hydrodynamic AMR simulations I discuss the effects of protostellar outflow feedback on low mass star formation in a turbulent molecular cloud. I compare the distribution of stellar masses, accretion rates, multiplicity and temperatures in simulations with and without protostellar outflow feedback.