Retrieving evidence to support or refute claims is a core part of automatic fact-checking. Prior work makes simplifying assumptions in retrieval that depart from real-world use cases: either no access to evidence, access to evidence curated by a human fact-checker, or access to evidence published after a claim was made. In this work, we present the first realistic pipeline to check real-world claims by retrieving raw evidence from the web. We restrict our retriever to only search documents available prior to the claim’s making, modeling the realistic scenario of emerging claims. Our pipeline includes five components: claim decomposition, raw document retrieval, fine-grained evidence retrieval, claim-focused summarization, and veracity judgment. We conduct experiments on complex political claims in the ClaimDecomp dataset and show that the aggregated evidence produced by our pipeline improves veracity judgments. Human evaluation finds the evidence summary produced by our system is reliable (it does not hallucinate information) and relevant to answering key questions about a claim, suggesting that it can assist fact-checkers even when it does not reflect a complete evidence set.