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Lattice simulations of the QCD correlation functions in the Landau gauge haveestablished two remarkable facts. First, the coupling constant in the gaugesector remains finite and moderate at all scales, suggesting that some kind ofperturbative description should be valid down to infrared momenta. Second, thegluon propagator reaches a finite nonzero value at vanishing momentum,corresponding to a gluon screening mass. We review recent studies which aim atdescribing the long-distance properties of Landau gauge QCD by means of theperturbative Curci-Ferrari model. The latter is the simplest deformation of theFaddeev-Popov Lagrangian in the Landau gauge that includes a gluon screeningmass at tree-level. There are, by now, strong evidences that this approachsuccessfully describes many aspects of the infrared QCD dynamics. Inparticular, several correlation functions were computed at one- and two-looporders and compared with {\it ab-initio} lattice simulations. The typical erroris of the order of ten percent for a one-loop calculation and drops to fewpercents at two loops. We review such calculations in the quenchedapproximation as well as in the presence of dynamical quarks. In the lattercase, the spontaneous breaking of the chiral symmetry requires to go beyond acoupling expansion but can still be described in a controlled approximationscheme in terms of small parameters. We also review applications of theapproach to nonzero temperature and chemical potential.

A window on infrared QCD with small expansion parameters