The ISCSLP 2024 Conversational Voice Clone (CoVoC) Challenge aims to benchmark and advance zero-shot spontaneous style voice cloning, particularly focusing on generating spontaneous behaviors in conversational speech. The challenge comprises two tracks: an unconstrained track without limitation on data and model usage, and a constrained track only allowing the use of constrained open-source datasets. A 100-hour high-quality conversational speech dataset is also made available with the challenge. This paper details the data, tracks, submitted systems, evaluation results, and findings.