Accretion of gas from the cosmic web to galaxy halos and ultimately their disks is a prediction of modern cosmological models but is rarely observed directly or at the full rate expected from star formation. Here we illustrate possible large-scale cosmic HI accretion onto the nearby dwarf starburst galaxy IC10, observed with the VLA and GBT. We also suggest that cosmic accretion is the origin of sharp metallicity drops in the starburst regions of other dwarf galaxies, as observed with the 10-m GCT. Finally, we question the importance of cosmic accretion in normal dwarf irregulars, for which a recent study of their far-outer regions sees no need for, or evidence of, continuing gas buildup.