The context of mediation immediately highlights the importance of argumentation as a means to reasonably handle conflict. Argumentation in dispute mediation tackles this topic providing both theoretical insights and detailed empirical argumentative analysis. Its goal is twofold: to explore mediation as a real-life context of argumentation and to show how an increased argumentative awareness could improve conflict resolution. Particular emphasis is accorded to mapping mediation through an interdisciplinary reasoned review of existing accounts. The outline of a conceptual framework of mediation constitutes a solid basis for the study of argumentation in mediation. The argumentative analysis of a corpus of mediation cases, based on the pragma-dialectical account and the Argumentum Model of Topics, shows the mediator's moves which actually help conflicting parties discuss reasonably. The mediator's topical potential plays a crucial role in this relation at the levels of issue selection, evoking of cultural-contextual premises and choice of argument schemes.