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The security of classical cryptog-raphy based on computational complexity as-sumptions has been severely challenged with the rapid development of quantum computers and quantum algorithms. Quantum cryptogra-phy, which offers unconditional security based on some principles of quantum mechanics, has become a significant branch and hotspot in the field of mod cryptography research. In this paper, we review the research and devel-opment of several important and well-studied branches of quantum cryptography in terms of theory and experiment, including quantum key distribution, quantum secret sharing, quantum secure direct communication, quantum sig-nature, and quantum private query. We also briefly review the research and development of some other branches which are currently in the stage of theoretical research but receive widespread conc from academia, including quantum private comparison, quantum anony-mous voting, quantum secure multi-party sum-mation, quantum sealed-bid auction, quantum public key cryptosystem, quantum key agree-ment, quantum dialogue, and quantum identity authentication. In addition, we discuss some open issues and future research directions for the branches referred to above.