Abstract: A fracton is an unusual new type of emergent quasiparticle, first proposed in the context of quantum phases of matter, which does not have the ability to move by itself. Rather, fractons can only move by forming certain bound states. In this talk, I will show that symmetric tensor gauge theories provide a natural theoretical framework for fractons, with the unusual mobility restrictions encoded in a set of higher moment charge conservation laws, such as conservation of dipole moment. I will then show how the tensor gauge theory formalism identifies ordinary elasticity theory as the first clear realization of fracton physics, while also shedding light on the physics of supersolids. Finally, I will discuss experimental signatures which can be used to identify emergent tensor gauge theory physics in the context of spin liquids.