Chasing the Unicorn: RHIC and the QGP

At nonzero temperature, it is expected that QCD undergoes a phase transition to a deconfined, chirally symmetric phase, the Quark-Gluon Plasma (QGP). I review what we expect theoretically about this possible transition, and what we have learned from heavy ion experiments at RHIC. I argue that while there are unambiguous signals for qualitatively new behavior at RHIC, versus experiments at lower energies, that in detail, no simple theoretical model can explain all salient features of the data.