Discourse Processing here is framed as marking up a text with structural descriptions on several levels, which can serve to support many language-processing or text-mining tasks. We first explore some ways of assigning structure on the document level: the logical document structure as determined by the layout of the text, its genre-specific content structure, and its breakdown into topical segments. Then the focus moves to phenomena of local coherence. We introduce the problem of coreference and look at methods for building chains of coreferring entities in the text. Next, the notion of coherence relation is introduced as the second important factor of local coherence. We study the role of connectives and other means of signaling such relations in text, and then return to the level of larger textual units, where tree or graph structures can be ascribed by recursively assigning coherence relations. Taken together, these descriptions can inform text summarization, information extraction, discourse-aware sentiment analysis, question answering, and the like.