I will describe the connection between quantum entanglement and (areas of) codimension-2 extremal surfaces in asymptotically AdS spacetimes,

which arises in the context of the AdS/CFT correspondence. Following a brief overview, I will turn to properties of a class of codimension-2 surfaces in these geometries, describing features that can be understood from the global Lorentz structure. I will also outline, time permitting, an interesting application of flow lines and the max-flow min-cut principle in this context.