Fact-checking complex claims refers to the systematic verification of real-world statements that cannot be validated by a single piece of evidence and instead require multi-step reasoning across multiple sources. Unlike simple fact-checking, which confirms straightforward, atomic assertions through direct lookups, evaluating complex claims involves decomposing multifaceted statements into simpler sub-tasks or intermediate questions. These sub-tasks are then addressed through targeted information retrieval and logical, numerical, or contextual analysis before the resulting evidence is synthesized to determine the overall veracity of the claim and generate an interpretable explanation of the verification process.