Equation of state and phase diagram of strongly interacting matter

In this work progress on the phase structure and the dynamics of strongly correlated matter with continuum methods is reviewed. First we discuss the set-up of functional approaches to correlation functions in QCD. Particular emphasis is put on the discussion of the mechanisms of confinement and chiral symmetry breaking in such an approach, as well as the embedding of low energy effective theories.Then, results are discussed concerning the confinement–deconfinement and the chiral phase transition at finite temperature and density. The present correlation function approach also allows to compute real-time correlations, including pole masses, decay constants, spectral functions and transport coefficients.