The explosive growth of machine learning has made it a critical infrastructure in the era of artificial intelligence. The extensive use of data poses a significant threat to individual privacy. Various countries have implemented corresponding laws, such as GDPR, to protect individuals' data privacy and the right to be forgotten. This has made machine unlearning a research hotspot in the field of privacy protection in recent years, with the aim of efficiently removing the contribution and impact of individual data from trained models. The research in academia on machine unlearning has continuously enriched its theoretical foundation, and many methods have been proposed, targeting different data removal requests in various application scenarios. However, recently researchers have found potential privacy leakages of various of machine unlearning approaches, making the privacy preservation on machine unlearning area a critical topic. This paper provides an overview and analysis of the existing research on machine unlearning, aiming to present the current vulnerabilities of machine unlearning approaches. We analyze privacy risks in various aspects, including definitions, implementation methods, and real-world applications. Compared to existing reviews, we analyze the new challenges posed by the latest malicious attack techniques on machine unlearning from the perspective of privacy threats. We hope that this survey can provide an initial but comprehensive discussion on this new emerging area.