Abstract: Trust management is an authorization mechanism for large-scale, open-distributed systems. Aspects of the trust management problem include formulating security policies and security credentials, determining whether particular sets of credentials satisfy the relevant policies, and deferring trust to third parties. Proof of compliance is a key problem in trust management problems, and certificate chain discovery is a key problem in proof of compliance. In this paper, the research on certificate chain discovery is described, certificate storage and certificate chain discovery algorithm are analyzed, future development directions about certificate chain discovery is pointed out.