In the age of Big Data, data is at the core of innovation, driving growth across industries such as healthcare, finance, retail, government, and the Internet of Things (IoT). However, this data deluge has caused critical concerns regarding human freedoms such as the privacy of individuals. As we collect, store, and analyze vast amounts of data, maintaining the balance between data utility and privacy becomes increasingly challenging and expensive. This paper provides a comprehensive exploration of privacy-preserving techniques and their applications, including traditional methods like k-anonymity, l-diversity, and t-closeness, as well as advanced approaches such as differential privacy, homomorphic encryption, and privacy-preserving machine learning. We investigate their historical development, real-world applications across various sectors, and the ethical challenges they pose, particularly in the context of Generative AI and Big Data analytics. The objective is to underscore how these techniques can enable the utilization of data without infringing on individual rights, ensuring in this way compliance with legal frameworks like GDPR and HIPAA. This paper also highlights research directions and future trends, emphasizing the importance of interdisciplinary collaboration in advancing privacy preservation while fostering innovation.