The broadly hierarchical material structure of the universe invites the reductionist question whether, at every level of the hierarcy, laws and regularities at lower levels can explain those at higher levels. This question has not been systematically asked using a Nagelian model of reduction. This paper surveys the state of work on this problem and tries to identify stages at which the reductionist program demonstrably fails. These constitute the major transitions in organization but they are few and far between.