If we are to have knowledge of the external world, the nature of that knowledge turns on the particular relations that we bear to the external world. One of the important roles played by skeptical arguments is that of narrowing down the relevant relations; skeptical arguments seem to show that some relations to the world do not obtain and thus that knowledge of the external world, if we are to have it, must not involve these relations. My dissertation focuses on this role of skeptical arguments. I first systematically determine which types of arguments for external world skepticism are the best, then examine which relations these arguments target. I conclude that the two best types of argument for external world skepticism are (i) arguments that turn on claims about the nature of evidential support and (ii) arguments that turn on the prevalence of lottery-like situations. I also conclude that the best arguments for external world skepticism target relations that are either"internal" (i.e. reflectively accessible) or "maximal" (i.e. at the extreme point along a certain scale). My conclusions are an important first step in discovering which relations we bear to the external world and thus what knowledge of the external world, if we are to have it, will amount to.