We survey Natural Language Processing (NLP) approaches to summarizing, simplifying, and generating patents' text. While solving these tasks has important practical applications - given patents' centrality in the R&D process - patents' idiosyncrasies open peculiar challenges to the current NLP state of the art. This survey aims at a) describing patents' characteristics and the questions they raise to the current NLP systems, b) critically presenting previous work and its evolution, and c) drawing attention to directions of research in which further work is needed. To the best of our knowledge, this is the first survey of generative approaches in the patent domain.