Cloud computing provides outsourcing of computing services at a lower cost, making it a popular choice for many businesses. In recent years, cloud data storage has gained significant success, thanks to its advantages in maintenance, performance, support, cost, and reliability compared to traditional storage methods. However, despite the benefits of disaster recovery, scalability, and resource backup, some organizations still prefer traditional data storage over cloud storage due to concerns about data correctness and security. Data integrity is a critical issue in cloud computing, as data owners need to rely on third-party cloud storage providers to handle their data. To address this, researchers have been developing new algorithms for data integrity strategies in cloud storage to enhance security and ensure the accuracy of outsourced data. This article aims to highlight the security issues and possible attacks on cloud storage, as well as discussing the phases, characteristics, and classification of data integrity strategies. A comparative analysis of these strategies in the context of cloud storage is also presented. Furthermore, the overhead parameters of auditing system models in cloud computing are examined, considering the desired design goals. By understanding and addressing these factors, organizations can make informed decisions about their cloud storage solutions, taking into account both security and performance considerations.