Classical Einstein gravity is expected to emerge as a low-energy effective theory from the fundamental degrees of freedom of a theory of quantum gravity. AdS/CFT gives us a precise definition of what those primitive degrees of freedom are (namely, the boundary CFT), thus leading to the question: how do features of classical (or semiclassical) gravity in the bulk emerge from boundary data? In my talk I'll briefly review this field of bulk reconstruction, and then discuss some recent work showing how in three dimensions, a large class of gravitational area laws can be interpreted precisely as arising from a coarse-graining over IR boundary field theory data; strong subadditivity of entanglement entropy then produces the area laws. If time permits, I'll discuss generalizations to higher dimensions, quantum extensions, and related work on recovering bulk metric data from boundary entanglement.