Computing has been widely used for data storage and computational purposes. When the authors discuss about the cloud storage services, the data must be outsourced, so, there may be serious concerns about the authorization and trust management for the Cloud Service Provider (CSP). These concerns are about confidentiality, integrity, security and access control. In this paper, they are going to discuss various models in brief such as Provable Data Possession (PDP), Proof Of Retrievability (POR), and HAIL, attribute based encryption scheme, Plutus, SiRiUS, Third Party Auditor (TPA) etc. that are introduced for addressing such issues about cloud storage systems.