Red supergiants (RSGs) are an He-burning phase in the evolution of moderately massive stars (10-25 Msun). For many years, the assumed physical properties of these stars placed them at odds with the predictions of evolutionary theory. We have recently determined new effective temperatures and luminosities for the RSG populations of galaxies with a factor of ~8 range in metallicity, including the Milky Way, the Magellanic Clouds, and M31. We find that these new physical properties greatly improve the agreement between the RSGs and the evolutionary tracks, although there are still notable difficulties with modeling the physical properties of RSGs at low metallicity. We have also examined several unusual RSGs, including VY CMa in the Milky Way, WOH G64 in the LMC, and a sample of four RSGs in the Magellanic Clouds, that show considerable variations in their physical parameters, most notably their effective temperatures. For all of these stars we re-examine their placement on the H-R diagram, where they have appeared to occupy the "forbidden" region to the right of the Hayashi track. We have updated current understanding of the physical properties of VY CMa and WOH G64; in the case of the unusual Magellanic Cloud variables, we conclude that these stars are undergoing an unstable evolutionary phase not previously associated with RSGs.