  The Green's functions of QCD encode important information about the infrared
dynamics of the theory. The main non-perturbative tools used to study them are
their own equations of motion, known as Schwinger-Dyson equations, and
large-volume lattice simulations. We have now reached a point where the
interplay between these two methods can be most fruitful. Indeed, the quality
of the lattice data is steadily improving, while a recently introduced
truncation scheme for the Schwinger-Dyson equations makes their predictions far
more reliable. In this talk several of the above points will be reviewed, with
particular emphasis on how to enforce the crucial requirement of gauge
invariance at the level of the Schwinger-Dyson equations, the detailed
mechanism of dynamical gluon mass generation and its implications for the ghost
sector, the non-perturbative effective charge of QCD, and the indirect
extraction of the Kugo-Ojima function from existing lattice data.
