With the development of cloud computing, a large number of individuals and companies transfer their data and business to cloud computing. But the management of the data and services of the cloud may not be fully trustworthy. How to ensure the integrity of data stored in cloud attracts more and more attention. A number of data files authentication and integrity schemes have been conducted to recognize any modification in the exchange of data files between two entities within a cloud environment. Existing solutions are based on combining key-based hash function with traditional factors (steganography, smart-card, timestamp). However, none of the proposed schemes appear to be sufficiently designed as a secure scheme to prevent from attacks. In recent years, lots of efficient and safe solutions to ensure the outsourced data integrity are proposed. This paper provides a survey of the main research results of the previous studies.