QCD Green's Functions and Phases of Strongly-Interacting Matter

After presenting a brief summary of functional approaches to QCD at vanishing temperatures and densities the application of QCD Green’s functions at non-vanishing temperature and vanishing density is discussed. It is pointed out in which way the infrared behavior of the gluon propagator reflects the (de-)confinement transition. Numerical results for the quark propagator are given thereby verifying the relation between (de-)confinement and dynamical chiral symmetry breaking (restoration). Last but not least some results of Dyson-Schwinger equations for the color-superconducting phase at large densities are shown.