In the contemporary landscape of big data analytics, privacy concerns loom large, exacerbated by escalating surveillance measures. This review delves into the advancements of privacy-enhancing technologies (PETs) amidst this era of heightened scrutiny. The review explores the evolving landscape of PETs, highlighting their pivotal role in safeguarding individual privacy while enabling meaningful data analysis. Firstly, the review elucidates the escalating surveillance environment, characterized by ubiquitous data collection practices and the proliferation of sophisticated monitoring mechanisms. Against this backdrop, the imperative for robust privacy solutions becomes evident. Subsequently, the review navigates through the array of PETs, encompassing differential privacy, homomorphic encryption, secure multi-party computation, and federated learning, among others. Each technology is scrutinized for its efficacy in mitigating privacy risks without compromising analytical utility. Furthermore, the review delineates notable applications of PETs across diverse domains, including healthcare, finance, and social media. Case studies exemplify how PETs facilitate data sharing and collaborative analysis while preserving confidentiality and compliance with regulatory frameworks. Moreover, the review examines the challenges hindering the widespread adoption of PETs, such as computational overhead, interoperability issues, and regulatory ambiguities. Strategies for overcoming these hurdles are elucidated, encompassing advancements in algorithmic efficiency, standardization efforts, and policy advocacy. The review underscores the pivotal role of PETs in reconciling the imperatives of data analytics with the imperatives of privacy protection amidst escalating surveillance. It emphasizes the necessity for interdisciplinary collaboration among researchers, policymakers, and industry stakeholders to foster the development and deployment of effective PET solutions, thereby ensuring a harmonious balance between data utility and individual privacy rights in the digital age.