People love to argue. In recent years, Artificial Intelligence has achieved great advances in modelling natural language argumentation. While analysing and creating arguments is a highly complex (and enjoyable!) task at which even humans are not good, let alone perfect, we describe our natural language processing (NLP) research to identify arguments, their stance and aspects, aggregate arguments into topically coherent clusters, and finally, even to generate new arguments, given their desired topic, aspect and stance. The talk will tell you the story how the ArgumenText project has been conceptualized into a set of novel NLP tasks and highlight their main research outcomes. Argument mining has a tremendous number of possible applications, of which the talk discusses a few selected ones.