"Throughout the whole life of the universe only 4% of the baryons have been converted into stars, implying that some physical processes must be responsible for suppressing star formation in galaxies. Within this context, one of the most hotly debated open questions is the identification of the process responsible for quenching star formation in galaxies and transforming them into passive and quiescent (gas poor) systems. Theories of galaxy formation have proposed various possible mechanisms, such as: gas removal by powerful outflows or ram pressure stripping, heating and photoionization of the interstellar medium, turbulent or gravitational quenching, halting of the gas supply inflow (often referred to as "strangulation"). The relevance and relative role of these mechanisms (as a function of cosmic epoch, galaxy properties and environment), especially at high redshift, are not yet understood because the constraints provided by current observational data have not yet been able to discriminate between different scenarios.In the proposed project I will make use of some of the most advanced observational facilities that will be available in the coming years to tackle this major outstanding open issue. More specifically, I will exploit the James Webb Space Telescope, MOONS (the next generation multi-object spectrograph at the ESO-VLT) and the Atacama Large Millimeter Array (ALMA).Observing programs making use of these unique facilities will provide an unprecedented amount of information, with unprecedented quality, that will enable us to discriminate between various quenching and feedback processes proposed by theories. More specifically, the aim of this project is to identify and quantify the dominant quenching and feedback mechanisms in galaxies as a function of redshift, as a function of galaxy properties and as a function of environment. The groundbreaking results of this project will be a benchmark for any model of galaxy evolution."