Arguing is amenable to humans and argumentation serves as anatural form of interaction in many settings. Several formal mod-els of argumentation have been proposed in the AI literature asabstractions of various forms of debates. We show how these mod-els can serve as the backbone of conversational systems that canexplain machine-computed outputs. These systems can engage inconversations with humans following templates instantiated onargumentation models that are automatically obtained from thedata analysis underpinning the machine-computed outputs. Asan illustration, we consider one such argumentation-empoweredconversational system and exemplify its use and benefits in twodifferent domains, for recommending movies and hotels based onthe aggregation of information drawn from reviews.