Abstract: Cipher computable encryption system refers to a series of designated functional operation which can be performed on encrypted data. The biggest difference with the traditional encryption system is the ciphertext is no longer"chaos", but has some hidden relations. The ciphertext can be the input of speciifc function and after function calculates the encrypted input, the output can become the effective information of users. Due to the direct computation on encrypted data, cipher computable encryption system greatly improves the efficiency of the availability of information under the encrypted condition, it has become the hot direction of modern public key cryptography research. This paper gives the detailed overview on three cipher computable encryption schemes of the predicate encryption, fully homomorphic encryption and functional encryption, introducing relations among different cipher computable encryption systems, analyzing the function privacy and application requirements about practical cipher computable encryption system and providing guidance for future research.