  We discuss the QCD phase structure at finite temperature and chemical
potential for $2$-flavour and $2+1$-flavour QCD. The results are achieved by
computing QCD correlation functions within a generalised functional approach
that combines Dyson-Schwinger equations (DSE) and the functional
renormalisation group (fRG). In this setup fRG precision data from
arXiv:1706.06326 for the vacuum quark-gluon vertex and gluon propagator of
$2$-flavour QCD are used as input, and the respective DSEs are expanded about
this input. While the vacuum results for other correlation functions serve as a
self-consistency check for functional approaches, the results at finite
temperature and density are computed, for the first time, without the need of
phenomenological infrared parameters.
