  Cosmological numerical simulations of galaxy evolution show that accretion of
metal-poor gas from the cosmic web drives the star formation in galaxy disks.
Unfortunately, the observational support for this theoretical prediction is
still indirect, and modeling and analysis are required to identify hints as
actual signs of star-formation feeding from metal-poor gas accretion. Thus, a
meticulous interpretation of the observations is crucial, and this
observational review begins with a simple theoretical description of the
physical process and the key ingredients it involves, including the properties
of the accreted gas and of the star-formation that it induces. A number of
observations pointing out the connection between metal-poor gas accretion and
star-formation are analyzed, specifically, the short gas consumption time-scale
compared to the age of the stellar populations, the fundamental metallicity
relationship, the relationship between disk morphology and gas metallicity, the
existence of metallicity drops in starbursts of star-forming galaxies, the
so-called G dwarf problem, the existence of a minimum metallicity for the
star-forming gas in the local universe, the origin of the alpha-enhanced gas
forming stars in the local universe, the metallicity of the quiescent BCDs, and
the direct measurements of gas accretion onto galaxies. A final section
discusses intrinsic difficulties to obtain direct observational evidence, and
points out alternative observational pathways to further consolidate the
current ideas.
