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As there is a continuous delivery of big data, the researchers are showing interest in the applications of cloud computing concerning privacy, and security. On the other hand, many researchers and experts of cybersecurity have commenced on a quest for improving the data encryption to the models of big data and applications of cloud computing. Since many users of the cloud become public cloud services, confidentiality turns out to be a more compound problem. To solve the confidentiality problem, cloud clients maintain the data on the public cloud. Under this circumstance, Homomorphic Encryption (HE) appears as a probable solution, in which the information of the client is encrypted on the cloud in such a process that it permits few manipulation operations without decryption. The main intent of this paper is to present the systematic review of research papers published in the field of Fully Homomorphic Encryption (FHE) over the past 10 years. The encryption scheme is considered full when it consists of plaintext, a ciphertext, a keyspace, an encryption algorithm, and a decryption algorithm. Hence, the review mostly concentrates on reviewing more powerful and recent FHE. The contributions using different algorithms in FHE like Lattice-based, integer-based, Learning With Errors (LWE), Ring Learning With Errors (RLWE), and Nth degree Truncated polynomial Ring Units (NTRU) are also discussed. Finally, it highlights the challenges and gaps to be addressed in modeling and learning about competent, effectual, and vigorous FHE for the cloud sector and pays attention to directions for better future research. [ABSTRACT FROM AUTHOR]