Heavy Ion Collisions at RHIC and at the LHC: Physics Challenges

Five years after starting operation, the Relativistic Heavy Ion Collider RHIC has finished the discovery stage of its relativistic heavy ion program. Here, I discuss in a simplified way the main discoveries of RHIC and the central open questions, which arise from these results. How can one achieve further progress in studying QCD matter at the highest density in the upcoming era, when both RHIC and LHC will be operational? Rather than listing the richness of the discoveries made at RHIC and expected at the LHC, I try to identify those generic features of a heavy ion program at collider energies, which lie at the basis of further progress