With the rapid development of cloud computing, more and more data to be stored in the cloud storage servers. Cloud storage as a new type of storage services, with high scalability, high reliability, low cost, can be accessed anytime and anywhere features, provides a new model for mass data storage management. However, due to data are outsourcing to a cloud services provider, users are actually relinquishing the ultimate control over the fate of their data, so it faces many challenges. Data possession provability allows cloud users to verify whether their data are still integrally, validly and correctly preserved in Cloud Storage system, and whether they can obtain the data at anytime, anywhere. It is a challenging research problem of cloud storage security. This paper concluded data persistence proving model from some aspects such as general encryption scheme to the data, homomorphic encryption scheme, third-party audit (TPA) and so on. This paper discussed and summarized the existing data persistence proving schemes and models, and concluded a general model based on data persistence proving model of TPA (third-party audits).