In this chapter we discuss the methodological views of omas Kuhn and Paul Feyerabend, two philosophers of science who have had considerable impact on recent work on methodology. While both Kuhn and Feyerabend have a reputation as anti-methodologists and advocates of epistemological relativism, this is not an entirely accurate assessment of their views. Both oppose the idea that there is some single, invariant and binding method that provides scientists with an “algorithm” of theory-appraisal. Nevertheless, both continue to uphold a role for method in the pursuit of science. In the case of Kuhn we distinguish several phases of development of his account of method; and in the case of Feyerabend we argue that he is not the advocate of “anything goes”, as is commonly thought.