  Light-matter interactions are an established field that is experiencing a
renaissance in recent years due to the introduction of exotic coupling regimes.
These include the ultrastrong and deep strong coupling regimes, where the
coupling constant is smaller and of the order of the frequency of the light
mode, or larger than this frequency, respectively. In the past few years,
quantum simulations of light-matter interactions in all possible coupling
regimes have been proposed and experimentally realized, in quantum platforms
such as trapped ions, superconducting circuits, cold atoms, and quantum
photonics. We review this fledgling field, illustrating the benefits and
challenges of the quantum simulations of light-matter interactions with quantum
technologies.
