Argument mining is the research area aiming at extracting natural language arguments and their relations from text, with the final goal of providing machine-processable structured data for computational models of argument. This research topic has started to attract the attention of a small community of researchers around 2014, and it is nowadays counted as one of the most promising research areas in Artificial Intelligence in terms of growing of the community, funded projects, and involvement of companies. In this paper, we present the argument mining tasks, and we discuss the obtained results in the area from a data-driven perspective. An open discussion highlights the main weaknesses suffered by the existing work in the literature, and proposes open challenges to be faced in the future.