We introduce FinDVer, a comprehensive benchmark specifically designed to evaluate the explainable claim verification capabilities of LLMs in the context of understanding and analyzing long, hybrid-content financial documents. FinDVer contains 4,000 expert-annotated examples across four subsets, each focusing on a type of scenario that frequently arises in real-world financial domains. We assess a broad spectrum of 25 LLMs under long-context and RAG settings. Our results show that even the current best-performing system (i.e., GPT-4o) significantly lags behind human experts. Our detailed findings and insights highlight the strengths and limitations of existing LLMs in this new task. We believe FinDVer can serve as a valuable benchmark for evaluating LLM capabilities in claim verification over complex, expert-domain documents.