Data-driven innovation in healthcare, finance, and smart cities increasingly depends on sharing rich datasets, but such sharing raises severe privacy risks and regulatory challenges. Privacy-preserving data publishing (PPDP) seeks to release useful data while preventing re-identification and inference attacks. This paper presents a comprehensive survey of anonymization techniques for PPDP, spanning traditional models (k-anonymity, l-diversity, t-closeness, and pseudonymization) and modern approaches (differential privacy (DP), synthetic data generation, federated learning (FL), secure multi-party computation (SMPC), homomorphic encryption (HE), blockchain-based schemes, and quantum-safe cryptography). We propose a taxonomy that organizes these methods by privacy guarantees, data utility, scalability, and computational cost, and we provide a comparative analysis of their strengths, limitations, and typical application domains. The survey also reviews legal and ethical frameworks, with particular attention to general data protection regulation GDPR, health insurance portability and accountability act (HIPAA), and related regulations, and highlights emerging trends such as artificial intelligence (AI-driven) anonymization and privacy risks from large language models (LLMs) and quantum computing. Overall, the study shows that various techniques fail to protect all data scenarios so we need to create hybrid systems which will provide explainable anonymization solutions at different scales to protect privacy and maintain useful data utility.