I use simple thermodynamic reasoning to argue that at temperatures of order a trillion kelvin, QCD, the theory which describes strongly interacting particles such as protons and neutrons under normal conditions, undergoes a phase transition to a plasma of more elementary constituents called quarks and gluons. I review what is known about the plasma phase both from theoretical calculations and from experiments involving the collisions of large atomic nuclei moving at relativistic speeds. Finally I consider the behaviour of nuclear material under conditions of extreme density, and discuss possible exotic phenomena such as quark matter and color superconductivity.

Article for final year undergraduate physicists, to appear in "Contemporary Physics". 34 pages, 13 figures