We commonly say that some evidence supports a hypothesis or that some premise evidentially supports a conclusion. Both internalists and externalists attempt to analyze this notion of evidential support, and the primary purpose of this paper is to argue that reliabilist and proper functionalist accounts of this relation fail. Since evidential support is one component of inferential justification, the upshot of this failure is that their accounts of inferential justification also fail. In Sect. 2, I clarify the evidential support relation. In Sects. 3–5, I subject reliabilist and proper functionalist accounts of evidential support to various counterexamples. In Sect. 6, I show that the most promising ways to address these counterexamples aren’t very promising.