This chapter is devoted to explaining the notion of asymmetric fallibilism. Asymmetric fallibilism is the idea that we tend to be less fallible when we persuade ourselves that parts of our previous theories were wrong rather than when we advance a promissory new theory. Even though epistemically vulnerable, scientists rationally confide—given certain conditions—that they can identify the parts of previous theories that are wrong. However, they are fallible when they do this. Some philosophers of science (e.g. Larry Laudan and Dudley Shapere, among others) have tried to avoid this kind of fallibilism by providing a general theory of rationality that is both descriptive and normative. With this theory in hand, we would be able to identify when scientists have made the right decisions and when they have not regarding theory choice. I argue that this is an unpromising path. I also analyse two main challenges to the idea of asymmetric fallibilism: creationism and global climate change denialism. I argue that they are not such challenges and put forward the notion of ‘epistemic remnants’ to describe these kinds of challenges. I conclude the chapter with a reflection on the ontological and epistemological consequences of asymmetric fallibilism.