Evidence for the accretion of cold gas in galaxies has been rapidly accumulating in the past years. HI observations of galaxies and their environment have brought to light new facts and phenomena which are evidence of ongoing or recent accretion: 1) A large number of galaxies are accompanied by gas-rich dwarfs or are surrounded by HI cloud complexes, tails and filaments. It may be regarded as direct evidence of cold gas accretion in the local universe. It is probably the same kind of phenomenon of material infall as the stellar streams observed in the halos of our galaxy and M31. 2) Considerable amounts of extra-planar HI have been found in nearby spiral galaxies. While a large fraction of this gas is produced by galactic fountains, it is likely that a part of it is of extragalactic origin. 3) Spirals are known to have extended and warped outer layers of HI. It is not clear how these have formed, and how and for how long the warps can be sustained. Gas infall has been proposed as the origin. 4) The majority of galactic disks are lopsided in their morphology as well as in their kinematics. Also here recent accretion has been advocated as a possible cause. In our view, accretion takes place both through the arrival and merging of gas-rich satellites and through gas infall from the intergalactic medium (IGM). The infall may have observable effects on the disk such as bursts of star formation and lopsidedness. We infer a mean ``visible'' accretion rate of cold gas in galaxies of at least 0.2 Msol/yr. In order to reach the accretion rates needed to sustain the observed star formation (~1 Msol/yr), additional infall of large amounts of gas from the IGM seems to be required.

To appear in Astronomy & Astrophysics Reviews. 34 pages. Full-resolution version available at http://www.astron.nl/~oosterlo/accretionReview