The desire to protect privacy in cyberspace has promoted the design of anonymous communication systems. Anonymity ensures that users do not expose sensitive information such as identity and communication relationship when using Internet services. Different anonymous communication systems provide different strength of anonymity protection. How to quantify and compare the degree of anonymity has been an important research topic since its beginning. And now it is getting more and more attention, and becoming a new research focus, more researches and applications are necessary to be carried out. Anonymity metrics can help users understand the levels of protection achieved through anonymous communication systems, and help developers gain objective and scientific basis for designing and improving anonymous communication systems. A general framework for anonymity metrics research is presented, including anonymous communication technology, attacks against anonymous communication technology, anonymity metrics, and their relationships. This study surveyed the researches in anonymity metric field, looking for their development and characteristics. A variety of theories and methods of anonymity metrics were reviewed and summarized following the time line. Considering attacks against anonymous communication, the characteristics and mutual relations of typical metric methods were sorted out, analyzed, and compared. And the new progresses were introduced, looking forward to the research direction and development trend. The analysis shows that anonymity metrics help to determine whether anonymous communication systems can provide promised anonymity, the metrics are becoming more diverse, and the metrics based on information theory are the most widely used. With the large-scale deployment of anonymous communication systems such as Tor, evaluations for real practical systems and infrastructures based on statistical data have emerged. New anonymous technologies have been developed rapidly recently, how to extend the metrics to the emerging technologies and how to combine different metrics to adapt to the emerging systems are the new research directions with solid application prospects.