Expressing opinions and interacting with others on the Web has led to the production of an abundance of online discourse data, such as claims and viewpoints on controversial topics, their sources and contexts (e.g., events, entities). These data constitute a valuable source of insights for studies into misinformation spread, bias reinforcement, echo chambers or political agenda setting. While knowledge graphs of today enable data reuse and federation thus improving information retrieval and facilitating research and knowledge discovery in various fields, they do not store informatotion about claims and related online discourse data, making it difficult to access, query and reuse this wealth of information. In my talk, I will present recent work in collaboration with the Leibniz Institute of Social Sciences GESIS (Germany), on the construction of ClaimsKG - a knowledge graph of fact-checked controversial claims, which facilitates structured queries about their truth values, authors, dates, journalistic reviews and other kinds of metadata and provides ground truth data for a number of tasks relevant to the analysis of societal debates on the web. I will discuss perspectives on modelling claims in a generalized and contextualized manner, as well as related challenges such as claim disambiguation and the assessment of claim relatedness. I will present preliminary results on learning claim vector representations (embeddings) from ClaimsKG and their application for the task of automatic fact-checking.