XQCD 2018

I give an update on the phase structure of QCD at vanishing and finite temperature and density with functional methods. Specifically results are discussed for the confinement-deconfinement and chiral phase transitions, the nature of these transitions and their interrelation, as well as the thermodynamics and fluctuations observables of QCD. The results on correlation functions are also used for the computation of gluon spectral functions and transport coefficients, as well as an input for QCD-assisted transport equation. First results for skewness and kurtosis in a system passing through the phase boundary are presented.