Starting in 1860, there have been many attempts to document levels of ancient biodiversity using the fossil record. I review four attempts, starting with John Phillips in 1860, followed by Jack Sepkoski’s classic study from 1984. John Alroy’s 2008 work updates Sepkoski’s work but presents problems of its own. The final review is of a study by Fan et al. (2020) who used a supercomputer to produce the most detailed analysis of ancient biodiversity so far. The four studies taken together demonstrate how palaeontologists are using increasingly sophisticated statistical techniques and an improved geological time scale to address the limitations of the fossil record. But more than that, they reveal mass extinctions as powerful agents of biotic change. These events directly influence not only the level of the planet’s biodiversity, but also the composition of its biota.