The hypothesis relating mass extinctions of life on Earth to impacts of comets whose flux is partly modulated by the dynamics of the Milky Way Galaxy contains a number of postulates that can be tested by geologic evidence and statistical analyses. In an increasing number of cases, geologic evidence for impact (widespread impact debris and/or large impact craters) is found at times of mass extinction events, and the record of dated impact craters has been found to show a significant correlation with mass extinctions. Statistical analyses suggest that mass extinction events exhibit a periodic component of about 26 to 30 Myr, and periodicities of 30± 0.5 Myr and 35 ±2 Myr have been extracted from sets of well-dated impact craters. The evidence is consistent with periodic or quasi-periodic showers of impactors, probably Oort Cloud comets, with an approximately 30-Myr cycle. The best explanation for these proposed quasi-periodic comet showers involves the Sun’s vertical oscillation through the galactic disk, which may have a similar cycle time between crossings of the galactic plane.