The area of Knowledge Representation and Reasoning has been enriched during the past two decades with the addition of Argument-Based Reasoning Systems. Defeat between arguments is established by a combination of two basic elements: a conflict or defeat relation, and a preference relation on the arguments involved in this conflict. The research activities are centered in our abstract framework for argumentation, where two kinds of defeat are present, depending on the outcome of the preference relation. This framework also takes subarguments into account, leading to the formalization of well formed argumentation lines.