Patterns of phenotypic change documented in the fossil record offer the only direct view scientists have of evolutionary transitions arrayed over significant durations of time. What lessons should be drawn from these data, however, has proven to be rather contentious. Although we as paleontologists have made great progress in documenting the geological record of phenotypic evolution with greater thoroughness and sophistication, these successes have been limited by the use of verbal models of how phenotypes change. Descriptive terms such as “gradual” have been understood differently by different authors, and this has led to completely incompatible summary statements about the fossil record of morphological evolution. Here I argue that the solution to this ambiguity lies in insisting that different evolutionary interpretations be represented as explicit, statistical models of evolution. With such an approach, the powerful machinery of likelihood-based inference can be help resolve long-standing paleontological questions.Here I first review this approach and some aspects of its implementation. Then, I show how this approach leads to new traction on important issues in evolutionary paleobiology, including: understanding modes of evolution and determining their relative importance, separating evolutionary mode from tempo, assessing the evidence for hypotheses of punctuated change, and detecting adaptive evolution in the fossil record.