  The cold interstellar medium (ISM) plays a central role in the galaxy
evolution process. It is the reservoir that fuels galaxy growth via star
formation, the repository of material formed by these stars, and a sensitive
tracer of internal and external processes that affect entire galaxies.
Consequently, significant efforts have gone into systematic surveys of the cold
ISM of the galaxies in the local Universe. This review discusses the resulting
network of scaling relations connecting the atomic and molecular gas masses of
galaxies with their other global properties (stellar masses, morphologies,
metallicities, star formation activity...), and their implications for our
understanding of galaxy evolution. Key take-home messages are as follows: (1)
From a gas perspective, there are three main factors that determine the star
formation rate of a galaxy: the total mass of its cold ISM, how much of that
gas is molecular, and the rate at which any molecular gas is converted into
stars. All three of these factors vary systematically across the local galaxy
population. (2) The shape and scatter of both the star formation main sequence
and the mass-metallicity relation are deeply linked to the availability of
atomic and molecular gas. (3) Future progress will come from expanding our
exploration of scaling relations into new parameter space (in particular the
regime of dwarf galaxies), better connecting the cold ISM of large samples of
galaxies with the environment that feeds them (the circumgalactic medium in
particular), and understanding the impact of these large scales on the
efficiency of the star formation process on molecular cloud scales.
