 As we have seen, reduction has been conceived of as a relation that primarily holds between theories, properties, substances, concepts, or events. It has been described as an explanatory relation that can be cashed out in terms of derivation, and it could be tied to mechanistic or ontological dependence, supervenience and identity. It has been argued that theory-reduction is prior to ontological reduction; and it has been argued that ontological reduction is more fundamental than theory reduction. Reduction has been couched in structuralist, empiricist and functionalist frameworks, and it has been one of the core notions of theories defending one form or another of scientific unification. Most philosophers have abandoned this latter view. But even if the outlook for strong general reductionism, a form of reductionism that amounts to scientific as well as ontological unity might be dim, exploring the question of what it takes for a property or theory to reduce to another property or theory will help not only understand what the search for unity consists in, a search that dominated large parts of the philosophy of science in the last century; it will also help judging and understanding its rivals, such as non-reductive physicalism, versions of dualism, or even the recently defended rainforest pluralism (Wimsatt 1994). If we know the conditions imposed by the reduction relation on pairs of theories or properties, we will also know what these anti-reductionist theories are bound to deny.