Title: The evolution of the ISM from z~0 to 7

Abstract: In this talk, I will briefly review the latest constraints on the cosmic molecular gas content and its relation to the cosmic density of the SFR using different tracers of the interstellar medium (ISM), including dust continuum and CO, [CI] and [CII] line emission. In particular, I will focus on recent measurements of the molecular gas fraction, gas depletion timescales and cosmic density provided by the recent ALMA large programs ASPECS, ALPINE and REBELS, out to z~7.5. Finally, I will discuss how the newly resolved high-resolution observations of [CII] line emission of normal galaxies at z=5-7 from our ongoing ALMA campaigns, including the ALMA CRISTAL large program, are unveiling the mechanisms for early galaxy formation.