  Lattice-based investigations of two fundamental QCD quantities are described,
namely the gluon and quark propagators in Landau gauge. We have studied the
Landau gauge gluon propagator using a variety of lattices with spacings from a
= 0.17 to 0.41 fm. We demonstrate that it is possible to obtain scaling
behavior over a very wide range of momenta and lattice spacings and to explore
the infinite volume and continuum limits. These results confirm that the Landau
gauge gluon propagator is infrared finite. We study the Landau gauge quark
propagator in quenched QCD using two forms of the O(a)-improved propagator and
we find good agreement between these. The extracted value of the infrared quark
mass in the chiral limit is found to be 300 +/- 30 MeV. We conclude that the
momentum regime where the transition from nonperturbative to perturbative QCD
occurs is Q^2 approx 4GeV^2.
