Abstract: In these two talks, we will give an introduction to the replica trick and the use of defect CFT techniques for computing entanglement entropy in a general field theory. We will discuss how one can compute shape variations of the entanglement entropy using the displacement operator. This leads us naturally to consider second shape variations of the entanglement entropy, which are the subject of the recently discovered quantum null energy condition. Our results tell us that for interacting CFTs with a twist gap the quantum null energy condition is saturated. These two talks will be based upon forthcoming work.