Stars with individual luminosities more than a million times that of the sun are now being studied in a variety of contexts. Observational and theoretical ideas about the most luminous stars have changed greatly in the past few years. They can be observed spectroscopically even in nearby galaxies. They are not very stable; some have had violent outbursts in which large amounts of mass were lost. Because of their instabilities, these stars do not evolve to become red supergiants as less luminous stars do. Theoretical scenarios for the evolution of these most massive stars depend on the effects of turbulence and mixing combined with high radiation densities.