The paper analyses the main trends in the discussions about the notion of supervenience in the last decades, putting the emphasis in some crucial problems. The starting point will be the various concepts of supervenience proposed by Jaegwon Kim. Through them, we will identify a dramatic tension between the extremes of eliminativism and dualism (in general, pluralism), being placed in the middle of them the positions of a non-eliminativist reductionism and of a non-dualist epiphenomenism. The open options facing that tension (...) show a very peculiar and valuable sort of philosophical work which could be called “conceptual engineering”. (shrink)