  We report on recent numerical computations of the Landau gauge gluon and
ghost propagators as well as of the ghost-gluon vertex function in pure SU(3)
Yang-Mills theory and in full QCD on the lattice. Special emphasis is paid to
the low momentum region. In particular, we present new data for the gluon
propagator at momenta below 300 MeV. We also discuss different systematic
effects as there are finite-size, lattice discretization and Gribov copy but
also unquenching effects. A MOM-scheme running coupling \alpha_s(q^2) based on
the ghost-gluon vertex is calculated and found to decrease for momenta below
550 MeV, even though the renormalization constant of the vertex deviates only
weakly from being constant.
