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The Green's functions of QCD encode important information about the infrareddynamics of the theory. The main non-perturbative tools used to study them aretheir own equations of motion, known as Schwinger-Dyson equations, andlarge-volume lattice simulations. We have now reached a point where theinterplay between these two methods can be most fruitful. Indeed, the qualityof the lattice data is steadily improving, while a recently introducedtruncation scheme for the Schwinger-Dyson equations makes their predictions farmore reliable. In this talk several of the above points will be reviewed, withparticular emphasis on how to enforce the crucial requirement of gaugeinvariance at the level of the Schwinger-Dyson equations, the detailedmechanism of dynamical gluon mass generation and its implications for the ghostsector, the non-perturbative effective charge of QCD, and the indirectextraction of the Kugo-Ojima function from existing lattice data.

Scrutinizing the Green's functions of QCD: Lattice meets Schwinger-Dyson