The study of argumentation is transversal to several research domains, from philosophy to linguistics, from the law to computer science and artificial intelligence. In discourse analysis, several distinct models have been proposed to harness argumentation, each with a different focus or aim. To analyze the use of argumentation in natural language, several corpora annotation efforts have been carried out, with a more or less explicit grounding on one of such theoretical argumentation models. In fact, given the recent growing interest in argument mining applications, argument-annotated corpora are crucial to train machine learning models in a supervised way. However, the proliferation of such corpora has led to a wide disparity in the granularity of the argument annotations employed. In this paper, we review the most relevant theoretical argumentation models, after which we survey argument annotation projects closely following those theoretical models. We also highlight the main simplifications that are often introduced in practice. Furthermore, we glimpse other annotation efforts that are not so theoretically grounded but instead follow a shallower approach. It turns out that most argument annotation projects make their own assumptions and simplifications, both in terms of the textual genre they focus on and in terms of adapting the adopted theoretical argumentation model for their own agenda. Issues of compatibility among argument-annotated corpora are discussed by looking at the problem from a syntactical, semantic, and practical perspective. Finally, we discuss current and prospective applications of models that take advantage of argument-annotated corpora
