The theme of this talk is the interplay between entanglement and renormalization in quantum matter. I will begin by describing recent progress in computing entanglement properties of interesting ground states by focusing on the low energy physics. Then I will discuss how the results of such studies lead us naturally to consider certain classes of tensor network states that incorporate the interplay between entanglement and renormalization. Finally I will talk about the connections between such tensor network states and holographic duality, which is a correspondence between quantum field theory and quantum gravity. I will not assume any prior knowledge of holography and only basic familiarity with the ideas of entanglement and renormalization.