Cloud computing designates a big architectural change on the way to thin clients and accessible central facility of computing resources. Clients are more interested to outsource their data on commercial public clouds for more flexibility and to reduce economic investments. In clouds, there is no direct control over resources by clients, so the security of data privacy is at the sake, provided by service providers. Traditional cryptography techniques cannot impose privacy necessitated by cloud computing services. Powerful recently apprehended, Fully Homomorphic Encryption (FHE), a fully functional construct that can enable search over encrypted text. The Paper discussed different types of FHE schemes, including schemes based on integers and polynomial over the ring of integers. The paper also includes the basic steps needed to construct any FHE scheme. The schemes are explained, along with their pros and cons. The paper may contribute to the development of privacy-preserving schemes of Cloud Computing.