This paper introduces the problem of predicting semantic relations expressed by prepositions and develops statistical learning models for predicting the relations, their arguments and the semantic types of the arguments. We define an inventory of 32 relations, building on the word sense disambiguation task for prepositions and collapsing related senses across prepositions. Given a preposition in a sentence, our computational task to jointly model the preposition relation and its arguments along with their semantic types, as a way to support the relation prediction. The annotated data, however, only provides labels for the relation label, and not the arguments and types. We address this by presenting two models for preposition relation labeling. Our generalization of latent structure SVM gives close to 90% accuracy on relation labeling. Further, by jointly predicting the relation, arguments, and their types along with preposition sense, we show that we can not only improve the relation accuracy, but also significantly improve sense prediction accuracy.