Fully Homomorphic Encryption (FHE) has emerged as a critical cryptographic tool which supports computations on encrypted data without any decryption. It offers valuable privacy-preserving capabilities for secure data analysis, cloud computing and privacy preserving machine learning (PPML). This paper provides a systematic review of the evolution of FHE, from its starting point with the concept of privacy homomorphisms in 1978, to the modern and mature algorithms such as CKKS and BFV/BGV schemes, and to the combination between FHE and AI algorithms. We examine in the aspects of efficiency improvements, noise optimizations, and application-specific designs for machine learning models like logistic regression, neural networks, and tree-based models, support vector machines, Naive Bayes classifier. We also explore the integration of FHE with federated learning frameworks, large language models, and hardware accelerators such as GPUs and FPGAs. The survey highlights both the continuous achievements and challenges in scaling FHE for practical AI applications.