Numerical simulations predict that gas accretion from the cosmic web drives star formation in disks galaxies. The process is important in low mass haloes (< 1012 M⊙), therefore, in the early universe when galaxies were low mass, but also in dwarf galaxies of the local universe. The gas that falls in is predicted to be tenuous, patchy, partly ionized, multi-temperature, and large-scale; therefore, hard to show in a single observation. One of the most compelling cases for gas accretion at work in the local universe comes from the extremely metal poor (XMP) galaxies. They show metallicity inhomogeneities associated with star-forming regions, so that large starbursts have lower metallicity than the underlying galaxy. Here we put forward the case for gas accretion from the web posed by XMP galaxies. Two other observational results are discussed too, namely, the fact that the gas consumption time-scale is shorter than most stellar ages, and the systematic morphological distortions of the HI around galaxies.