QCD and high-energy nuclear collisions

Six years ago, Relativistic Heavy Ion Collider at Brookhaven started colliding heavy nuclei at record center-of-mass energies of up to 200 GeV/nucleon. Very soon, the Large Hadron Collider at CERN will push the energy of the ions to an astounding 5 TeV/nucleon. What can be learnt from the experiments at these machines? What do we know about the physics of super--dense matter already? I will argue that heavy ion accelerators bring us to the new frontiers of physical knowledge by creating strong color fields and very high densities of partons, at which qualitatively new phenomena emerge. I will also discuss the cross-disciplinary implications for cosmology, astrophysics, and connections to condensed matter physics.