  We review a burgeoning field of "fractons" -- a class of models where
quasi-particles are strictly immobile or display restricted mobility that can
be understood through generalized multipolar symmetries and associated
conservation laws. Focusing on just a corner of this fast-growing subject, we
will demonstrate how one class of such theories -- symmetric tensor and
coupled-vector gauge theories surprisingly emerge from familiar elasticity of a
two-dimensional quantum crystal. The disclination and dislocation crystal
defects respectively map onto charges and dipoles of the fracton gauge theory.
This fracton-elasticity duality leads to predictions of fractonic phases and
quantum phase transitions to their descendants, that are duals of the
commensurate crystal, supersolid, smectic, hexatic liquid crystals, as well as
amorphous solids, quasi-crystals and elastic membranes. We show how these dual
gauge theories provide a field theoretic description of quantum melting
transitions through a generalized Higgs mechanism. We demonstrate how they can
be equivalently constructed as gauged models with global multipole symmetries.
We expect extensions of such gauge-elasticity dualities to generalized
elasticity theories provide a route to discovery of new fractonic models and
their potential experimental realizations.
