Several calculations of the upward throughgoing and stopping muon fluxes produced by atmospheric, or cosmic ray, neutrinos interacting in the material surrounding underground detectors are compared and the uncertainties in the calculations estimated. We evaluate the implications for neutrino oscillations of the measured and calculated upward muon fluxes in relation to the neutrino oscillation interpretation of the atmospheric neutrino-induced interactions totally contained within the underground detectors. It appears that the region of the [Delta][ital m][sup 2], sin[sup 2]2[theta] parameter space excluded by previous analyses of the upward throughgoing muons has been overestimated, and that a more likely representation is consistent with the contained event result. In contrast, the region delineated by comparison of the observed and calculated stopping fractions is less ambiguous and comparable in quality with that obtained from the totally contained event samples.