  This paper discusses how cosmic gas accretion controls star formation, and
summarizes the physical properties expected for the cosmic gas accreted by
galaxies. The paper also collects observational evidence for gas accretion
sustaining star formation. It reviews evidence inferred from neutral and
ionized hydrogen, as well as from stars. A number of properties characterizing
large samples of star-forming galaxies can be explained by metal-poor gas
accretion, in particular, the relationship between stellar mass, metallicity,
and star formation rate (the so-called fundamental metallicity relationship).
They are put forward and analyzed. Theory predicts gas accretion to be
particularly important at high redshift, so indications based on distant
objects are reviewed, including the global star formation history of the
universe, and the gas around galaxies as inferred from absorption features in
the spectra of background sources.
