Bipartite ranking refers to the problem of learning a ranking function from a training set of positively and negatively labeled examples. Applied to a set of unlabeled instances, a ranking function is expected to establish a total order in which positive instances precede negative ones. The performance of a ranking function is typically measured in terms of the AUC. In this paper, we study the problem of multipartite ranking, an extension of bipartite ranking to the multi-class case. In this regard, we discuss extensions of the AUC metric which are suitable as evaluation criteria for multipartite rankings. Moreover, to learn multipartite ranking functions, we propose methods on the basis of binary decomposition techniques that have previously been used for multi-class and ordinal classification. We compare these methods both analytically and experimentally, not only against each other but also to existing methods applicable to the same problem.