A global description of heavy-ion collisions A careful determination of the conditions probed in ultrarelativistic heavy-ion collisions requires the analysis of more than one observable to yield unambiguous results. I present such an analysis for the example of central 158 AGeV Pb-Pb collisions at CERN SPS and for 200 AGeV Au-Au collisions at RHIC. Using constraints given by an analysis of the freeze-out state based on hadronic observables, the space-time expansion of fireball is parametrized. Assuming a thermalized system with isentropic expansion, the EoS as obtained in lattice QCD simulations can be used to calculate thermodynamic properties of the fireball. The resulting scenario is then tested by calculating several different observables within this evolution, including dilepton and photon radiation, J/Psi suppression, hadron abundancies and HBT parameters. In all cases, agreement with data is found. Specifically, the sensitivity of the individual observables to certain phases in the evolution history of the system is discussed.