This talk explores large-margin approaches to predicting graph-based objects like trees, clusterings, or alignments. Such problems arise, for example, when a natural language parser needs to predict the correct parse tree for a given sentence, when one needs to determine the co-reference relationships of noun-phrases in a document, or when predicting the alignment between two proteins. In particular, the talk will show how structural SVMs can learn such complex prediction rules, using the problems of supervised clustering, protein sequence alignment, and diversification in search engines as application examples. Furthermore, the talk will present new cutting-plane algorithms that allows training of structural SVMs in time linear in the number of training examples.