Understanding the process responsible for transforming star forming galaxies into passive and quiescent systems is currently one of the hottest topics in astronomy. I will discuss recent observational results probing different mechanisms at work in different galaxies and at different epochs. I will present multi-wavelength observations providing evidence that powerful starburst-driven and AGN-driven outflows have a profound impact on the evolution of galaxies, both locally and at high redshift; however such massive outflows may not be able to completely quench star formation in galaxies and actually, in some cases, such outflows can even boost star formation. I will show that the analysis of the stellar metallicities in large samples of local galaxies reveals that “strangulation” (or “starvation”, i.e. the lack of gas inflows) is actually responsible for quenching star formation in most galaxies. I will discuss the possible mechanisms responsible for the starvation of galaxies.