Argumentation is a communicative and interactional act aimed at resolving a di erence of opinion. The last two decades have seen a formal and computational turn in argumentation theory with the goal to automate di erent aspects of argumentation. This leads to several challenges from an AI perspective, including e cient algorithms that need to be designed to guarantee short response times of argumentation systems. In this talk, I rst give a broad overview on the area of computational argumentation and discuss shortcomings of current approaches. We then identify a particular leak in the popular argumentation-pipeline model, where con ict resolution is solely based on abstract arguments rather than on the arguments' claims. I will introduce a new formal model that shifts the focus from arguments to claims and give a comprehensive complexity analysis of several argumentation semantics under this claimcentric view. In addition, the talk addresses the complexity of sub-classes and presents novel parameterizations which exploit the nature of claims explicitly along with xed-parameter tractability results.