Symmetry allows us to make exact statements about strongly coupled systems, where theoretical tools are very limited. Appropriately generalizing symmetry can then lead to a powerful new set of tools. For this reason, generalized global symmetries have received much attention in quantum field theory and condensed matter physics over the last few years. In this talk, I will give a general overview of a type of generalized symmetry known as higher-form symmetry, a symmetry that acts on higher-dimensional objects rather than local operators. I will explain what higher-form symmetries are, providing several pedagogical examples. I will also discuss the consequences of breaking these symmetries spontaneously, demonstrating that certain phases of matter, commonly thought to be beyond the conventional symmetry-breaking framework, can be characterized by higher-form symmetries. I will further illustrate how higher-form symmetries can lead to new non-perturbative constraints. Finally, I will highlight ways in which higher-form symmetries are different from ordinary symmetries.
