A central challenge in condensed matter physics is to classify all phases of matter. Quantum information theory on the other hand provides a powerful framework for studying the pattern of entanglement which exists and persists in many body wavefunctions such as ground states of local Hamiltonians. The convergence of these two fields in recent years has not only given new insight into familiar results, but also spurred several significant discoveries. In this talk, I will demonstrate how ideas from quantum information theory enhance our understanding of quantum phases of matter, focusing on two key examples. First, I will discuss the robustness of topological memory, which concerns the stability of logical qubits encoded in the ground state of a topologically ordered material against local environmental errors. Second, I will examine measurement‐induced phase transitions, which emerge in monitored quantum systems evolving under a combination of scrambling unitaries and local measurements. I will then connect these ideas to my own work on charge‐sharpening transitions from the perspective of an emergent gauge theory, drawing a sharp parallel between these two sets of problems. Finally, I will introduce a new way of looking at entanglement dynamics that naturally arises from this framework that extends the membrane picture of entanglement growth in chaotic systems.