Fully homomorphic encryption (FHE) techniques allow a third party to do arbitrarily many computations on encrypted data without learning any extra information over the real data. With the homomorphism property many practical solutions can be realized including secure online storage, private search on data, and secure data mining. In this talk, we give a survey about the concepts of somewhat homomorphic encryption and bootstrappability, and techniques to obtain fully homomorphic encryption from these primitives. Finally, if time permits we will also discuss potential future work inluding efficient verification of FHE.