Nearly thirty years ago, Arthur and Clozel proved that every nilpotent Galois representation of a number field arises from an automorphic representation, which, in fact, follows from Artin reciprocity, their cyclic base change, and some group theory. In this talk, we will discuss what goes wrong when trying to apply the cyclic base change to attack general monomial Galois representations, and what one can do instead. In particular, we shall discuss how to derive Langlands reciprocity for any Galois representation whose image is either nearly nilpotent or "small'".