Over the entire life of the Universe only 4% of the baryons have been converted into stars, while gravitational collapse and gas cooling would predict that locally about 80% of the baryons should be in stars. Hence, rather than understanding how stars have formed throughout the cosmic times, it is more important to understand why stars have not formed. To keep the star formation efficiency low, most models of galaxy evolution invoke some form of negative feedback. In low mass galaxies most of the feedback is thought to be associated with outflows generated by SNe and/or radiation pressure. In massive galaxies an additional source of energetic feedback is required to quench star formation and to prevent these galaxies from overgrowing. Most models suggest that this additional feedback is ascribed to the nuclear accreting black holes reaching quasar-like luminosities, which should generate massive outflows cleaning the host galaxies of its gas content, hence quenching star formation.

While observational evidence for starburst-driven outflows has been known for several years, clear and direct observational evidence for quasar-driven massive and energetic outflows has been obtained only very recently through multi-wavelength observations. I will review these observational evidences of negative quasar feedback, both in the local universe and at high redshift. I will show how these observational results can constrain theoretical models of galaxy evolution. More generally, I will show that such massive molecular outflows, especially those at high redshift, can account for the observational properties of massive local galaxies. I will also discuss the case, proposed by some recent models, of positive feedback in the quasar-driven outflows, i.e. star formation triggered within the molecular outflow. If confirmed observationally this could be a new, alternative mode of galaxy formation. I will discuss the observational prospects of testing and investigating this scenario.