Paul Feyerabend and Thomas Kuhn both claimed that revolutionary scientific progress is the result of replacing a theory that was once taken to be true with an incommensurable rival. The two theories separated by a revolution are incommensurable because they have no common measure in the form of neutral evidence (measurements) that can be used to compare them empirically. After a brief overview that compares Feyerabend and Kuhn’s philosophies of science and situates incommensurability within each of their conceptions of scientific progress, the essay addresses the following questions: What is incommensurability? What causes it? What are its consequences for intelligibility? What does it imply about theory comparison? And finally, what does incommensurability imply about truth, reality, and progress?