Just as ordinary global symmetries are associated with a conserved particle number, quantum field theories with generalized global symmetries have a conserved density of higher-dimensional objects (such as strings, branes, etc.). I will review how such a generalized symmetry plays an important role in characterizing the long-distance physics of familiar Maxwell electrodynamics in four dimensions. I will then discuss the holographic duals of quantum field theories that possess such generalized symmetries. If time permits I will also explain how such continuous symmetries can be broken down to discrete subgroups, resulting in boundary Goldstone modes and a topological field theory in the bulk that captures the physics of the unbroken discrete symmetry.
