Lattice simulations of Yang-Mills theories and QCD in the Landau gauge have
demonstrated that the gluon propagator saturates at vanishing momentum. This can
be modeled by a massive deformation of the corresponding Faddeev-Popov
Lagrangian known as the Curci-Ferrari model. The latter does not modify the known
ultraviolet regime of the theory and provides a successful perturbative description of
essential aspects of the non-Abelian dynamics in the infrared regime, where, in
particular, the coupling remains finite, as also seen in lattice simulations. This opens
the possibility of a controlled (semi)perturbative description of various aspects of the
infrared QCD dynamics, ranging from correlation functions, to chiral symmetry
breaking or the deconfinement phase transition at finite temperature and density. I
review recent progress in this context.