Automated Claim Verification (CV)—the task of assessing a claim’s veracity against explicitly provided evidence—is a critical tool in the fight against growing misinformation. This survey offers a comprehensive analysis of 198 studies published between January 2022 and March 2025, synthesizing recent advances in CV corpus creation and system design. Through two in-depth case studies, we illuminate persistent challenges in veracity annotation, limitations of conventional CV pipelines, and pitfalls in recent claim decomposition approaches. We conclude by identifying key unresolved challenges and proposing productive directions for future research.