Protecting privacy of data is a critical issue when handling sensitive medical information and homomorphic encryption (HE) emerges as a promising method facilitating computation on encrypted data. However, securely and efficiently processing private information in cloud computing remains challenging. Fully Homomorphic Encryption (FHE) can be a possible solution to privacy issues such that untrusted third parties may process cipher data without compromising the confidentiality of information. FHE shall prove valuable in distributed computation environments where confidentiality and integrity of data is also equally important. This survey provides a comprehensive review of FHE on theoretical foundations, current developments, limitations, potential applications, and available tools. The survey also suggests that FHE can be combined with machine learning to enable efficient predictions while safeguarding patient data privacy.