Typical properties of glassy materials are shown to be captured by a mean-field free-volume theory. Relaxation processes are supposed to be free-volume activated, and different entropy barriers are associated with density relaxation and shear motion. Free-volume time logarithmic relaxation, Kohlrausch-Williams-Watts, and power law viscosity result from the non-linear dynamics of spatially averaged quantities. The exponents associated with these phenomena are related to a single parameter of the theory. The theory also accounts for coexistence of jamming transitions and non-linear rheology.