This survey provides an overview of homomorphic encryption (HE) schemes, focusing on their theory and implementation. HE allows third parties to perform computations on encrypted data without decrypting it, addressing privacy concerns in cloud computing and data sharing. The survey discusses the evolution of HE schemes, starting with Partially Homomorphic Encryption (PHE) and Somewhat Homomorphic Encryption (SWHE), which support limited operations, and culminating in Fully Homomorphic Encryption (FHE), which enables arbitrary computations on encrypted data. The first practical FHE scheme, introduced by Craig Gentry in 2009, was based on ideal lattices and allowed any computable function to be applied to encrypted data. However, early FHE schemes faced challenges in computational efficiency and practical implementation. The survey reviews key PHE, SWHE, and FHE schemes, their properties, and recent advancements, including improvements in FHE implementations. It also discusses the challenges and future directions in HE research, emphasizing the importance of HE in protecting privacy in cloud and data-centric environments. The survey aims to provide a comprehensive understanding of HE schemes for researchers and practitioners, covering both theoretical foundations and practical implementations.This survey provides an overview of homomorphic encryption (HE) schemes, focusing on their theory and implementation. HE allows third parties to perform computations on encrypted data without decrypting it, addressing privacy concerns in cloud computing and data sharing. The survey discusses the evolution of HE schemes, starting with Partially Homomorphic Encryption (PHE) and Somewhat Homomorphic Encryption (SWHE), which support limited operations, and culminating in Fully Homomorphic Encryption (FHE), which enables arbitrary computations on encrypted data. The first practical FHE scheme, introduced by Craig Gentry in 2009, was based on ideal lattices and allowed any computable function to be applied to encrypted data. However, early FHE schemes faced challenges in computational efficiency and practical implementation. The survey reviews key PHE, SWHE, and FHE schemes, their properties, and recent advancements, including improvements in FHE implementations. It also discusses the challenges and future directions in HE research, emphasizing the importance of HE in protecting privacy in cloud and data-centric environments. The survey aims to provide a comprehensive understanding of HE schemes for researchers and practitioners, covering both theoretical foundations and practical implementations.