When we search the literature, we usually describe what we want in our own terms, which may be expressed only implicitly in papers; our requirements grow as we read more; and sometimes the topic we seek is not covered by any existing work. To address these challenges, the authors introduce CompLit, a benchmark that spans all eight arXiv domains and provides a diagnostic setting for each of the three need types: implicit, cumulative, and unmet.\ \ Under standard queries, the strongest agents—Codex (GPT-5.6‑Sol) and Claude Code (Opus 4.8)—answer 86% and 87% of questions correctly. When requirements are implicit, their accuracy drops to 66%‑68%; with cumulative requirements, they lose another 6 and 15 percentage points respectively; and for unmet queries, the agents abstain on up to 53% of the cases.\ \ Performance varies across domains, and all agents are less accurate on papers published before 2019 or after 2023. Tracing their search trajectories shows that agents often reach the right paper—or the closest one—but misjudge its relevance.\ \ Achieving strong results on CompLit is a step toward trustworthy literature‑search agents that can either retrieve the needed paper or clearly indicate that no suitable paper exists.\ \ Review