  Ultrastrong coupling between light and matter has, in the past decade,
transitioned from theoretical idea to experimental reality. It is a new regime
of quantum light-matter interaction, going beyond weak and strong coupling to
make the coupling strength comparable to the transition frequencies in the
system. The achievement of weak and strong coupling has led to increased
control of quantum systems and applications like lasers, quantum sensing, and
quantum information processing. Here we review the theory of quantum systems
with ultrastrong coupling, which includes entangled ground states with virtual
excitations, new avenues for nonlinear optics, and connections to several
important physical models. We also review the multitude of experimental setups,
including superconducting circuits, organic molecules, semiconductor
polaritons, and optomechanics, that now have achieved ultrastrong coupling. We
then discuss the many potential applications that these achievements enable in
physics and chemistry.
