Numerical simulations predict that gas accretion from the cosmic web drives star formation in disks galaxies. The process is more important in low mass haloes, therefore, when galaxies were low mass in the early universe, but also in dwarf galaxies of the local universe. The central role played by cosmic gas infall is as clear from numerical simulations as it is obscure to observations. The gas that falls in is predicted to be tenuous, patchy, partly ionized, multi-temperature, low-metallicity, and large-scale; thus, 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 that then underlying galaxy. This and other evidence suggest that local XMP are primitive disks sustained by cosmic web gas accretion. In the contribution we described the case posed by XMP galaxies to support the existence of cosmological gas accretion.