The propensity interpretation of probability was introduced by Popper in 1957, and the chapter begins with a discussion of Popper’s initial account of propensities and a comparison with Peirce’s related ideas. The original propensity interpretation had a number of strands, some of which could be accepted while others were rejected. This meant that the propensity interpretation could be, and was, developed in different ways by different philosophers of science. One point at issue was whether propensities were objective probabilities of single events. This led to a distinction between (i) single-case propensity theories, and (ii) long-run propensity theories. Another problem concerned the relation between propensities and causes – if propensities had a causal import, because of what is known as the Humphreys’ paradox they might not satisfy the standard axioms of probability. The chapter concludes by discussing how propensities might be connected to observed frequencies via the theory of statistical testing.