Abstract In some respects, there is more agreement between Newton and Leibniz on the relativity of motion than is generally recognized. Both were convinced Copernicans, and both accepted that motion could not be a merely extrinsic denomination—there would have to be true motions, and not just apparent ones. And both sought to discriminate true from apparent motions by reference to the causes of motion and to force. Where they differed was in their radically divergent understandings of how causes are related to forces, of how forces are to be determined in relation to quantity of motion, and of the ontological status of absolute or mathematical space. This chapter aims to throw light on the two philosophers’ respective views on the relativity of motion by considering them in their historical genesis.