Atmospheric neutrinos produced by cosmic-ray interactions in the atmosphere are of interest for several reasons. As a beam for studies of neutrino oscillations they cover a range of parameter space hitherto unexplored by accelerator neutrino beams. The atmospheric neutrinos also constitute an important background and calibration beam for neutrino astronomy and for the search for proton decay and other rare processes. Here we review the literature on calculations of atmospheric neutrinos over the full range of energy, but with particular attention to the aspects important for neutrino oscillations. Our goal is to assess how well the properties of atmospheric neutrinos are known at present.