Over the past decade, it has become increasingly clear that there are deep connections between high energy physics and quantum information, with entanglement serving as a bridge. The Ryu-Takayanagi conjecture is one of the seminal results which translates questions about the entanglement entropy of a CFT state to the task of calculating the lengths of minimal geodesics. These computations are especially tractable for 1+1d CFTs, where there are a variety of additional symmetries. These states are dual to 2+1d solutions of Einstein's equations via the AdS/CFT correspondence, but we will not go into much detail about this in this talk. Instead, we will provide an overview of these connections as they are relevant to quantum information theorists. More specifically, we will outline some of the surprising aspects of entanglement entropy in this family of states and what is known about how they are described by MERAs. This talk will include many computer-generated images.