A pervasive aspect of human communication and sociality is argumentation: the practice of making and criticizing reasons in the context of doubt and disagreement. Argumentation underpins and shapes the decision-making, problem-solving, and conflict management which are fundamental to human relationships. However, argumentation is predominantly conceptualized as two parties arguing pro and con positions with each other in one place. This dyadic bias undermines the capacity to engage argumentation in complex communication in contemporary, digital society. This book offers an ambitious alternative course of inquiry for the analysis, evaluation, and design of argumentation as polylogue: various players arguing over many positions across multiple places. Taking up key aspects of the twentieth-century revival of argumentation as a communicative, situated practice, the polylogue framework engages a wider range of discourses, messages, interactions, technologies, and institutions necessary for adequately engaging the contemporary entanglement of argumentation and complex communication in human activities.