It has long been understood that the exact (“fundamental”) gauge symmetry of the electromagnetic fields plays an important role in the theory of quantum materials. What has come into focus more recently is that there exist essential properties of quantum phases of matter that are best understood in terms of an effective field theory with emergent gauge fields, rather than (or in addition to) in terms of broken symmetries. Here, gauge invariance is not a symmetry of the microscopic problem but is rather an efficient representation of the low energy physics. I will review the well-known usefulness of this perspective in the context of such old friends as fractional quantum Hall fluids and a variety of ``spin-liquids.’’ As time permits, I will also discuss recent theoretical results that suggest that exotic “resonating valence-bond” fluids, describable by emergent gauge theories, might exist in a much broader range of experimentally accessible platforms than has been previously appreciated.
