Abstract: Symmetry is not what we once believed it to be. The familiar language of invariance and groups captures only the tip of the iceberg. At a deeper level, symmetry is determined by the algebra of allowed local operators, which gives rise to a far richer structure -- encompassing higher-form, anomalous, and non-invertible symmetries. In this talk, I argue that groups are no longer the correct organizing principle for these operator algebras. Instead, I will show how the operator algebra naturally generate fusion and braiding structures, revealing that symmetries are shadows of topological order living in one higher dimension. This unexpected Symmetry/Topological-Order correspondence has radical consequences for how phases of matter and their phase transitions must be understood and classified.