Semi-quantum communication, a model introduced in 2007 by M. Boyer, D. Kenigsberg, and T. Mor (PRL 99 140501), involves the use of fully-quantum users and semi-quantum, or "classical" users. These restricted users are only allowed to interact with the quantum channel in a limited manner. Originally introduced to study the key-distribution problem, semi-quantum research has since expanded, and continues to grow, with new protocols, security proof methods, experimental implementations, and new cryptographic applications beyond key distribution. Research in the field of semi-quantum cryptography requires new insights into working with restricted protocols and, so, the tools and techniques derived in this field can translate to results in broader quantum information science. Furthermore, other questions such as the connection between quantum and classical processing, including how classical information processing can be used to counteract a quantum deficiency in a protocol, can shed light on important theoretical questions. This work surveys the history and current state-of-the-art in semi-quantum research. We discuss the model and several protocols offering the reader insight into how protocols are constructed in this realm. We discuss security proof methods and how classical post-processing can be used to counteract users' inability to perform certain quantum operations. Moving beyond key distribution, we survey current work in other semi-quantum cryptographic protocols and current trends. We also survey recent work done in attempting to construct practical semi-quantum systems including recent experimental results in this field. Finally, as this is still a growing field, we highlight, throughout this survey, several open problems that we feel are important to investigate in the hopes that this will spur even more research in this topic.

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