In this paper we consider fully homomorphic encryption based on the learning with errors problem. We present the problem as introduced by Oded Regev in 2009 and explain a simple public key cryptosystem based on it. We show how the scheme can be modified to be more suitable for homomorphic operations, and introduce bootstrapping, using the ideas proposed by Craig Gentry in 2009. Finally we examine bootstrapping techniques proposed by Chilotti et al. in 2016, which is the main topic of this paper.