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In this talk I will consider quantum states satisfying an area law for entanglement (e.g. as found in quantum field theory or in condensed matter systems at sufficiently low temperature). I will show that both the boundary state and the entanglement spectrum admit a local description whenever there is no topological order. The proof is based on strong subadditivity of the von Neumann entropy. For topological systems, in turn, I'll show that the topological entanglement entropy quantifies exactly how many extra bits are needed in order to have a local description for the boundary state. This latter result is based on a recent strengthening of strong subadditivity. Based on joint work with Kohtaro Kato (University of Washington)