We will give a survey of recent work on lattice-based cryptography, mainly focusing on the so-called Learning with Errors (LWE) problem. This problem has turned out to be an amazingly versatile basis for cryptographic constructions, with tens of applications, including the recent celebrated work on fully homomorphic encryption. In addition to applications, we will also mention very recent work providing a better understanding of the security of the problem. The talk does not require any prior knowledge in cryptography or in lattices.