Cloud computing has become a prominent technology due to its important utility service; this service concentrates on outsourcing data to organizations and individual consumers. Cloud computing has considerably changed the manner in which individuals or organizations store, retrieve, and organize their personal information. Despite the manifest development in cloud computing, there are still some concerns regarding the level of security and issues related to adopting cloud computing that prevent users from fully trusting this useful technology. Hence, for the sake of reinforcing the trust between Cloud Clients (CC) and Cloud Service Providers (CSP), as well as safeguarding the CC’s data in the cloud, several security paradigms of cloud computing based on a Third-Party Auditor (TPA) have been introduced. The TPA, as a trusted party, is responsible for checking the integrity of the CC’s data and all the critical information associated with it. However, the TPA could become an adversary and could aim to deteriorate the privacy of the CC’s data by playing a malicious role. In this paper, we present the state-of-art of cloud computing’s privacy-preserving models (PPM) based on a TPA. Three TPA factors of paramount significance have been discussed: TPA involvement, security requirements, and security threats caused by vulnerabilities. Moreover, TPA’s privacy preserving models have been comprehensively analyzed and categorized into different classes with an emphasis on their dynamicity. Finally, we discuss the limitations of the models and present our recommendations for their improvement.