Past research has shown that the energy released by accreting super massive black holes (SMBHs) and by intense star formation activity can undermine even the coldest and densest phase of the interstellar medium (ISM), namely the cold molecular gas, which represents the main fuel for star formation. Massive molecular outflows, with velocities approaching 1000 km/s, outflow mass-loss rates of 100s of MSun/yr and sizes of several kiloparsecs, have been observed in the host galaxies of powerful starbursts and quasars from redshift, z~0 up to z>6. Explaining the presence of such large masses of cold dense gas in outflow and understanding their driving mechanisms is the goal of extensive ongoing theoretical and observational efforts, which I will review in this talk. I will also discuss the interpretation of these outflows as main players of the baryon cycle in and out of galaxies, in which they may have a two-fold role: immediate quenching of star formation in the central kiloparsecs, and long-term feeding of the galaxy by injecting (cold) gas in the circumgalactic medium.