The study of phases of matter and the transitions between them has been a central enterprise in physics for well over a century. One of the earliest paradigms for elucidating phase structure, associated most with Landau, classifies phases according to the spontaneous breaking of global symmetries present in a physical system. More recently, we have also made great strides in understanding topological phases of matter which lie outside Landau's framework: the order in topological phases cannot be characterized by local patterns of symmetry breaking, and is instead encoded in global patterns of quantum entanglement.