In the 1970s and 1980s, a number of scientists set out to show that paleontology could make important contributions to our understanding of how evolution works at large scales. The new research program(s) that emerged during this exciting period had an uneasy relationship with Darwin’s ideas. For example, paleontologists challenged the assumption that natural selection is sufficient to explain larger-scale patterns and trends in the fossil record. Those trends might result from passive diffusion away from a fixed boundary, or perhaps from the differential extinction, persistence, and branching of entire lineages. In this project, however, I argue that there is another important (though less obvious) way of thinking about what the paleobiologists were up to. They were engaging critically with the Darwinian tradition by raising questions about our default expectations with respect to evolutionary processes. This is easiest to see in the case of Eldredge and Gould’s theory of punctuated equilibria (PE), which challenged the idea that gradual morphological change should be our default expectation when we approach the fossil record. Eldredge and Gould famously argued that stasis is the dominant theme of evolutionary history, but early critics of PE complained that they had left stasis itself something of a mystery. What sorts of evolutionary mechanisms could explain why stasis characterizes so many lineages for most of their duration? Is stasis the default expectation for evolving lineages? Is it something like an inertial state? Or is stasis a surprising phenomenon that needs to be explained by appeal to specific evolutionary forces, such as stabilizing selection? This debate about stasis is a good starting point for assessing what was going on during the paleobiological revolution.