  In Landau gauge QCD the Kugo-Ojima confinement criterion and its relation to
the infrared behaviour of the gluon and ghost propagators are reviewed. It is
demonstrated that the realization of this confinement criterion (which is
closely related to the Gribov-Zwanziger horizon condition) results from quite
general properties of the ghost Dyson-Schwinger equation. The numerical
solutions for the gluon and ghost propagators obtained from a truncated set of
Dyson--Schwinger equations provide an explicit example for the anticipated
infrared behaviour. The results are in good agreement, also quantitatively,
with corresponding lattice data obtained recently. The resulting running
coupling approaches a fixed point in the infrared, $\alpha(0) = 8.915/N_c$.
Solutions for the coupled system of Dyson--Schwinger equations for the quark,
gluon and ghost propagators are presented. Dynamical generation of quark masses
and thus spontaneous breaking of chiral symmetry takes place. In the quenched
approximation the quark propagator functions agree well with those of
corresponding lattice calculations. For a small number of light flavours the
quark, gluon and ghost propagators deviate only slightly from the ones in
quenched approximation. While the positivity violation of the gluon spectral
function is manifest in the gluon propagator, there are no clear indications of
analogous positivity violations for quarks so far.
