Phase transitions in quantum chromodynamics

The current understanding of finite-temperature phase transitions in QCD is reviewed. A critical discussion of refined phase-transition criteria in numerical lattice simulations and of analytical tools going beyond the mean-field level in effective continuum models for QCD is presented. Theoretical predictions about the order of the transitions are compared with possible experimental manifestations in heavy-ion collisions. Various places in phenomenological descriptions are pointed out where more reliable data for QCD's equation of state would help in selecting the most realistic scenario among those proposed. Unanswered questions are raised about the relevance of calculations that assume thermodynamic equilibrium. Promising new approaches for implementing nonequilibrium aspects of the thermodynamics of heavy-ion collisions are described.