Molecular gas is the medium from which stars form. To date, a few hundreds of galaxies at z>1 have been observed in their molecular gas emission, typically traced via rotational transitions of the carbon monoxide, CO. The vast majority of these galaxies was pre-selected based on their stellar mass, star formation rate, and/or nuclear activity. Molecular scans (adopted in programs such as ASPECS and COLDz) offer a novel look at the gas content of high-redshift galaxies, by sampling CO emission ample volumes of the universe without any pre-selection of the targeted galaxies. State-of-the-art campaigns using >100 hr of ALMA and VLA successfully measured the total gas mass of typical galaxies up to z~3. This allowed us to directly connect the cosmic history of star formation with the gas content in galaxies. However, to date, these blank field investigations of molecular gas have been limited by modest statistics. A transformational step in terms of survey speed is mandatory in order to go beyond cosmic averaged quantities. The next generation Very Large Array will be instrumental in order to accurately measure the shape of the CO luminosity functions, and to test how the molecular gas reservoirs changes as a function of nuclear activity, metallicity, galactic environment, and other properties.