Method and apparatus are disclosed for heterogeneous data storage management in cloud computing. According to some embodiments, a method for managing data storage in a communication network comprises: receiving at a data center in the communication network from a first device, a request for storing a data in the data center; checking whether the same data has been stored in the data center; in response to a check result that no same data has been stored in the data center, receiving from the first device a data package containing at least the data in plaintext or ciphertext (CT) in response to a check result that the same data has been stored in the data center, obtaining a deduplication policy for the data; when the deduplication policy indicates deduplication to be controlled by both or either of an authorized party (AP) and an owner of the data, or only the AP, or only the data owner, contacting both or either of the AP and the data owner, or only the AP, or only the data owner to conduct deduplication for the data; and when the deduplication policy indicates deduplication to be controlled by none of the AP and the data owner, conducting deduplication for the data at the data center. In some embodiments, the data package may contain or indicate the deduplication policy, and contain information for data holdership verification. The data center may challenge to ensure the data holdership before contacting to conduct deduplication or conducting deduplication at the data center.