This habilitation thesis collects works addressing several challenges on handling uncertainty and inconsistency in knowledge representation. In particular, this thesis contains works which introduce quantitative uncertainty based on probability theory into abstract argumentation frameworks. The formal semantics of this extension is investigated and its application for strategic argumentation in agent dialogues is discussed. Moreover, both the computational as well as the meaningfulness of approaches to analyze inconsistencies, both in classical logics as well as logics for uncertain reasoning is investigated. Finally, this thesis addresses the implementation challenges for various kinds of knowledge representation formalisms employing any notion of inconsistency tolerance or uncertainty.