  The emergent field of cavity quantum materials bridges collective many-body
phenomena in solid-state platforms with strong light-matter coupling in cavity
quantum electrodynamics (cavity QED). This brief review provides an overview of
the state of the art of cavity platforms and highlights recent theoretical
proposals and first experimental demonstrations of cavity control of collective
phenomena in quantum materials. This encompasses light-matter coupling between
electrons and cavity modes, cavity superconductivity, cavity phononics and
ferroelectricity, correlated systems in a cavity, light-magnon coupling, cavity
topology and the quantum Hall effect, as well as superradiance. An outlook of
potential future developments is given.
