Argumentation represents the study of views and opinions that humans express with the goal of reaching a conclusion through logical reasoning. Since the 1950's, several models have been proposed to capture the essence of informal argumentation in different settings. With the emergence of the Web, and then the Semantic Web, this modeling shifted towards ontologies, while from the development perspective, we witnessed an important increase in Web 2.0 human-centered collaborative deliberation tools. Through a review of more than 150 scholarly papers, this article provides a comprehensive and comparative overview of approaches to modeling argumentation for the Social Semantic Web. We start from theoretical foundational models and investigate how they have influenced Social Web tools. We also look into Semantic Web argumentation models. Finally we end with Social Web tools for argumentation, including online applications combining Web 2.0 and Semantic Web technologies, following the path to a global World Wide Argument Web.