QCD propagators and vertices from lattice QCD (in memory of Michael M\"uller-Preu{\ss}ker)

We review lattice calculations of the elementary Greens functions of QCD with a special emphasis on the Landau gauge. These lattice results have been of interest to continuum approaches to QCD over the past 20 years. They are used as reference for Dyson-Schwinger- and functional renormalization group equation calculations as well as for hadronic bound-state equations. The lattice provides low-energy data for propagators and three-point vertices in Landau gauge at zero and finite temperature even including dynamical fermions. We summarize Michael M"uller-Preu{\ss}ker’s important contributions to this field and put them into the perspective of his other research interests.