Privacy-preserving data processing refers to the methods and models that allow computing and analyzing sensitive data with a guarantee of confidentiality. As cloud computing and applications that rely on data continue to expand, there is an increasing need to protect personal, financial and healthcare information. Conventional centralized data processing methods expose sensitive data to risk of breaches, compelling the need to use decentralized and secure data methods. This paper gives a detailed review of privacy-saving mechanisms in the cloud platform, such as statistical approaches like differential privacy and cryptographic solutions like homomorphic encryption. Federated analytics and federated learning, two distributed learning frameworks, are also discussed. Their principles, applications, benefits, and limitations are reviewed, with roles of use in the fields of healthcare, finance, IoT, and industrial cases. Comparative analyses measure trade-offs in security, efficiency, scalability, and accuracy, and investigations are done of emerging hybrid frameworks to provide better privacy protection. Critical issues, including computational overhead, privacy-utility trade-offs, standardization, adversarial threats, and cloud integration are also addressed. This review examines in detail the recent privacy-protecting approaches in cloud computation and offers scholars and practitioners crucial information on secure and effective solutions to data processing.