Understanding how galaxies form and evolve requires knowledge of their cold gas component, and how this depends on their structural and star formation properties, as well as large-scale environment. Significant effort has gone into large, dedicated observing campaigns that have measured the atomic and molecular hydrogen content of sizeable samples of galaxies on global and local scales, and placed these in the context of their optical and star-formation properties as well as environments. Despite these efforts, much remains to be learned about the physical drivers of these relations and how the global cold gas properties of galaxies are linked to the local process of star formation, as well as how these relations evolve with cosmic time. In this talk I will discuss how ongoing surveys of atomic and molecular gas content of galaxies -- from global to kpc scales and from nearby to higher redshift systems -- are advancing this field and conclude with a forward outlook on Square Kilometer Array science in this area.