Deep surveys performed with millimetric telescopes and with the Infrared Space Observatory have partly resolved the Cosmic IR Background (CIRB) into a population of IR sources characterized by extremely high rates of cosmological evolution (comparable to or higher than those observed for quasars). We report in this paper on early attempts to study these sources and to understand their physics. The IR multi-wavelength galaxy statistics can be explained by assuming, for the bulk of the IR population, spectra typical of starbursts, an indication that stellar more than quasar activity produces the IR emission by faint galaxies. From our fits to the observed optical-IR SEDs, the latter appear to mostly include massive galaxies hosting violent starbursts (SFR ~ 100 M⊙/yr). We interpret the strong redshift-evolution as an increase with z of the rate of interactions between galaxies (density evolution) and an increase of their IR luminosity due to the more abundant fuel available in the past (luminosity evolution). Our evolutionary scheme considers a bimodal star formation (SF) in galaxies, including long-lived quiescent SF, and enhanced SF taking place during transient events triggered by interactions and merging. The large energy content in the CIRB may possibly require a top-heavy stellar IMF associated with the starburst phase. The observed evolution of galaxy IR emissivity is so strong from z=0 to z ~ 1 that the CIRB spectral shape imposes a fast turnover to the evolution at z > 1: scenarios in which a relevant fraction of stellar formation occurs at very high-z (e.g., the bulk of stars in spheroids) are not supported by our analysis.