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.