Models of galaxy formation predict that gas accretion from the cosmic web is a primary driver of star formation over cosmic history. Except in very dense environments where galaxy mergers are also important, model galaxies feed from cold streams of gas from the web that penetrate their dark matter haloes. Although these predictions are unambiguous, the observational support has been indirect so far. I will report spectroscopic evidence for this process in extremely metal-poor galaxies (XMPs) of the local Universe, taking the form of localized starbursts associated with gas having low metallicity. Because gas mixes azimuthally in a rotation timescale (a few hundred Myr),  the observed metallicity inhomogeneities are only possible if the metal-poor gas producing stars fell onto the disk recently. I will analyze several possibilities for the origin of the metal-poor gas, favoring the metal-poor gas infall predicted by numerical models. In addition, I will show model galaxies in cosmological numerical simulations with starbursts of low metallicity like to the star-forming regions in XMPs.