The Formation of Massive Stars Massive stars, those larger than 20 times the mass of the Sun, are very rare, but their extreme luminosities make them both the only type of young star we can observe in distant galaxies and the dominant energy sources in the universe today. How such stars form, however, is a longstanding mystery. Efficient radiative cooling in the dense clouds where massive stars form should favor fragmentation into objects of solar mass or smaller. Even if a collapsing cloud exceeds this mass, massive stars produce so much light that the radiation pressure they exert on the gas and dust around them is stronger than their gravitational attraction, a condition that has long been expected to prevent them from growing by accretion. I discuss recent simulations that suggest that we have finally solved these two problems, work made possible by the development of numerical algorithms for 3D adaptive mesh radiation-hydrodynamics on parallel supercomputers. I also propose direct observational tests of these results.