Fully homomorphic encryption is a cryptography system in which coded data can be searched and statistically processed without decryption. Fully homomorphic encryption has accelerated searching speed by minimizing time spent on encryption and decryption. In addition, it is also known to prevent leakage of any data decoded for statistical reasons. Also, it is expected to protect personal information stored in the cloud computing environment which is becoming commercialized. Since the 1970s when fully homomorphic encryption was first introduced, it has been researched to develop the algorithm that satisfy effectiveness and functionality. We will take the reader through a journey of these developments and provide a glimpse of the exciting research directions that lie ahead.