The notion of potentiality was central in Aristotelian philosophy, which scholastic thinkers heavily relied on. Nonetheless, the notion of a natural potentiality increasingly lost its explanatory relevance in the later middle ages, or so I will argue here with regard to Aquinas, Scotus and Ockham. While this notion plays a pivotal role in Aquinas's account of contingency and natural teleology, Scotus and Ockham tried to account for these phenomena without appeal to natural potentialities of substances. Instead they maintained that contingency arises from the free operation of the will and that processes can only be teleologically directed towards certain ends if they are performed or arranged with an awareness of these ends by a rational agent. In this vein, late medieval authors tended to deprive natural potentialities of some of their explanatory tasks and assigned them to the rational capacities of God and other rational beings.