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.