QCD at high density/temperature

QCD now occupies an established position as the well-attested theory of strong-interaction physics. Other contributions to these proceedings (those of S. Frixione, L. Lellouch, and K. Long) survey the agreement between evidence from particle collider experiments and perturbative and lattice QCD calculations. However, there is more to QCD than collisions between pairs of particles. QCD should also be able to tell us about the thermodynamics of matter in the realm of extraordinarily high temperatures (& 100 MeV) and densities at which it comes to dominate the behavior. This regime has real physical importance: the whole universe was hotter than 100 MeV for the first crucial microseconds of its history, and in the current epoch our galaxy has a large population of neutron stars consisting of matter squeezed beyond nuclear density by gravitational forces. However, only in the last few years have these regimes begun to be probed experimentally in heavy ion collisions and astrophysical observations of neutron stars, and we are still working towards achieving a proper theoretical understanding of them. In this paper I will survey the progress that has been made in the last few years in qualitative predictions and quantitative calculations of the properties of QCD at very high temperature and net baryon density. I will not discuss theory that is specifically tailored to heavy ion collisions, but refer the reader to existing review articles [1]. Other more tightly focused reviews of QCD at CFL liq QGP T