Federated learning (FL) is a distributed machine learning approach that enables data processing at the edge nodes, offering significant benefits in terms of data privacy, scalability, and robustness. However, FL faces several critical challenges, particularly in privacy preservation, communication efficiency, security, system and statistical heterogeneity as advanced technologies continue to evolve. Privacy preservation in FL becomes increasingly complex with the risk of data leakage through gradients, inference attacks, and sophisticated threats like membership inference and GAN-based attacks. Addressing these challenges is essential to enhance the applicability of FL in real-world scenarios. This paper provides a comprehensive overview of federated learning, addressing key challenges and exploring various privacy-preserving methods, including homomorphic encryption, secure multi-party computation, and differential privacy. This paper also examines how advanced techniques, such as game theory and three-way decision-making, can enhance privacy and security in federated learning systems. It proposes future research directions to develop more secure, efficient, and scalable FL frameworks, ultimately facilitating the broader adoption of FL in practical applications through robust privacy-preserving techniques.