It is unlikely that a hacker is able to compromise sensitive data that is stored in an encrypted form. However, when data is to be processed, it has to be decrypted, becoming vulnerable to attacks. Homomorphic encryption fixes this vulnerability by allowing one to compute directly on encrypted data. In this survey, both previous and current Somewhat Homomorphic Encryption (SHE) schemes are reviewed, and the more powerful and recent Fully Homomorphic Encryption (FHE) schemes are comprehensively studied. The concepts that support these schemes are presented, and their performance and security are analyzed from an engineering standpoint.