This dissertation studies the fascinating interaction between quantum information theory and many-body physics. While the laws and principles of quantum mechanics are well known and can be formulated in compact equations, understanding many-body physics and the emergent phenomena related to it gives rise to a whole new set of challenges. In this dissertation we contribute to this field by showing how in three different domains perspectives from quantum information theory and computation can be useful in the study of many-body physics. In the first part of the thesis it is shown that a certain class of quantum circuits which implement real-space renormalization accurately capture ground states of one-dimensional free quantum systems. This approach uses wavelet theory. The second part of the thesis considers one-dimensional quantum dynamics which preserve locality in an approximate manner. Such dynamics are completely classified, using methods from operator algebra theory, by an index measuring information flow. In the third and final part of the dissertation, a toy model for holographic quantum gravity is investigated. This model is a tensor network model with random tensors. Conjectured relations between information theoretic quantities in holographic quantum gravity can be rigorously proven in this setting.