The star-formation activity of the Universe has gone through strong changes from redshifts of z~3 until present day. Information about the gas content of typical star-forming galaxies responsible for these changes has so far largely been missing. In this talk I present several theoretical approaches to make predictions for and support upcoming observations of the gas content of high redshift galaxies with ALMA and SKA. First, I present a novel method to indirectly estimate the HI and H2 content of a sample of ~20000 galaxies covering a wide range of redshifts and highlight the HI and H2 evolution in this sample of galaxies. Second, I present a new model in which I explicitly track the formation of molecular hydrogen and implement a physically-motivated H2-based star formation recipe within a semi-analytic cosmological galaxy formation model. I discuss our predictions for the atomic and molecular content of galaxies, how they evolve and how they constrain our understanding of galaxy formation and evolution. Third, I present a combination of this model of galaxy formation with a three-dimensional radiative transfer code. I discuss the CO, HCN, C, [CII], and [OI] emission from galaxies and use this tool to study how the detailed gas properties of galaxies during cosmic noon compares to galaxies in the local Universe and make direct predictions for ALMA observations.