In this talk we will be reviewing the two main theories about discourse representation, namely Rhetorical Structure Theory (RST) and Segmented Discourse Representation Theory (SDRT) as well as presenting computational models for the predictions of such structures. As it often happens in many Computational Linguistics problems, so also in discourse the objects to be learned cannot be cast into simple binary or n-ary classes. Instead a sequence, tree or more complicated structures such as graphs need to be predicted by an underlying model. The second part of this talk will be focused on the presentation of such structured output prediction methods. We will be using SDRT as our underlying theory in order to build discourse models for multi-party chat dialogues in the context of the game “Settlers of Catan”.