The phase structure of QCD can be explored with functional methods.
The challenge is to devise and solve an appropriate truncation of the corresponding
equations. Here the application to theories similar to QCD but
without the sign problem of lattice methods (QCD-like theories) becomes
useful, as truncations can be tested by comparison to corresponding lattice
results also at nonvanishing density. The universality of a certain class of
truncations is shown for three di?erent theories including QCD. Going one
step further, results for the quark-gluon vertex, the main model input of
most contemporary studies, will be shown.