Shape descriptor is a concise and informative representation. Feature extraction is a key step in many 3D shape analysis tasks. In recent years, feature extraction technologies of non-rigid 3D shape have attracted a lot of attentions. This paper firstly introduces the evaluation criteria and the datasets which are commonly used as benchmark in non-rigid 3D shape feature extraction. Secondly, based on extensive research on the existing literatures and the latest achievements, the paper categorizes the non-rigid 3D shape descriptors into two types:Hand-Crafted shape descriptors and learning based shape descriptors. The basic ideas, advantage and disadvantage of typical algorithms belong to each category, especially the most recent feature extraction algorithms based on deep learning are analyzed, compared and summarized. Finally, some potential future work is discussed.