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.