When the Universe was Hot and Sticky

The phase diagram of Quantum Chromodynamics (QCD, the theory of the strong interaction) is only poorly known. There are currently vibrant experimental and theoretical programs that concentrate on the production, study, and characterization of the quark-gluon plasma: a fundamental state of matter that existed a few microseconds after the Big Bang. I will describe the theoretical aspects of this endeavour, and highlight some of the surprises uncovered along the way.