  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 GTC. 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.
