Argument(ation) Mining (AM) is the dimension of computational argumentation aiming at automatically processing natural language arguments and reason upon them. More precisely, argument mining aims at extracting, classifying and analysing natural language arguments and their relations from text, with the final goal of providing machine-processable structured data for computational models of argument. In this keynote talk, I will first introduce this research area, highlighting the main successful tasks and open issues in identifying argumentative structures from different kinds of texts (e.g., clinical trials, online user generated content, news articles). Then, I will present a key challenge which conjugate argument mining with formal computational models of argumentation, i.e., the assessment of the trustworthiness of natural language arguments, with a focus on fallacious argumentation, with the aim to show how these methods can be used to automatically identify fallacious arguments in political debates. Fallacies play a prominent role in argumentation since antiquity due to their contribution to argumentation in critical thinking education. Their role is even more crucial nowadays as contemporary argumentation technologies face challenging tasks as misleading and manipulative information detection in news articles and political discourse, and counter-narrative generation. I will conclude with some thoughts on the challenge of automatic generation of counter-arguments to fight online disinformation and hate speech.