Schrödinger probably had a cat, but he surely coined the concept of entanglement as the general characterization of quantum correlations. In his words (1935): "the best possible knowledge of a whole does not necessarily include the best possible knowledge of all its parts." The theory of entanglement has then been mainly developed in quantum information theory, where it serves as a universal resource for the different tasks (e.g. quantum computation). But one of the key evolutions in physics in the last decade has been the realization that entanglement is actually important for all fields that involve quantum phenomena, like condensed matter physics, high energy physics and even quantum gravity. The formalism of tensor network states (TNS) is one of the groundbreaking developments that emerged in this context. It provides an entirely novel language for the understanding and simulation of quantum many body systems in terms of their entanglement properties. In this project we want to further advance the 'entanglement program' for quantum field theories (QFT), that for instance appear in the Standard Model of particle physics. We will address diverse questions like: How do symmetries affect the entanglement properties? What is the entanglement of empty space? Can we encode the entanglement at different length scales in an extra emerging dimension? And how does this all help us to for specific challenging problems, like the numerical simulation of non-equilibrium physics?Schrödinger probably had a cat, but he surely coined the concept of entanglement as the general characterization of quantum correlations. In his words (1935): "the best possible knowledge of a whole does not necessarily include the best possible knowledge of all its parts." The theory of entanglement has then been mainly developed in quantum information theory, where it serves as a universal resource for the different tasks (e.g. quantum computation). But one of the key evolutions in physics in the last decade has been the realization that entanglement is actually important for all fields that involve quantum phenomena, like condensed matter physics, high energy physics and even quantum gravity. The formalism of tensor network states (TNS) is one of the groundbreaking developments that emerged in this context. It provides an entirely novel language for the understanding and simulation of quantum many body systems in terms of their entanglement properties. In this project we want to further advance the 'entanglement program' for quantum field theories (QFT), that for instance appear in the Standard Model of particle physics. We will address diverse questions like: How do symmetries affect the entanglement properties? What is the entanglement of empty space? Can we encode the entanglement at different length scales in an extra emerging dimension? And how does this all help us to for specific challenging problems, like the numerical simulation of non-equilibrium physics?