Abstract: TRE (timed-release encryption) is a cryptographic primitive where the sender encrypts a message to prevent from being decrypted by anyone, including the designated receiver, until a future pre-set release time specified by the sender. Some other extensions make TRE have time properties of decrypting in advance and decrypting in a time interval. Since many applications in practice are time-sensitive, such as sealed-bid auctions, mortgage payments, on-line examinations and electronic confidential archives, TRE is considered as a valuable cryptographic tool. By summarizing existing TRE schemes and analyzing their characteristics, we give the formal definition and security goals definition of TRE. On the top of that, we introduce three fundamental frameworks of TRE along with their related mathematical problems, and further describe some typical constructions. We comprehensively analyze the security goals (specifically the message confidentiality and message unforgeability) of TRE, as well as their security bound under the adaptive chosen-plaintext attack and adaptive chosen-ciphertext attack models. Finally, we conduct research on the application of TRE; especially propose the preconditions and generic schemes for combining TRE with other cryptographic mechanisms. And we also construct a concrete scheme of public key timed-release searchable encryption which is a combination of TRE and public key encryption with keyword search. The future research directions in TRE are discussed in addition.