There is now a large consensus that the current epoch of the Cosmic Star Formation History (CSFH) is dominated by low mass galaxies while the most active phase at 1~1, the most IR-luminous galaxies (LIRGs and ULIRGs) are preferentially located in groups, and this is consistent with a reversal of the star-formation rate vs .density anti-correlation observed in the nearby Universe. At these redshifts, group galaxies contribute 60-80% of the CSFH, i.e. much more than at lower redshifts. Below z~1, the comoving number and SFR densities of IR-emitting galaxies in groups decline significantly faster than those of all IR-emitting galaxies. Our results are consistent with a "halo downsizing" scenario and highlight the significant role of "environment" quenching in shaping the CSFH.