  Enhancing optical nonlinearities so that they become appreciable on the
single photon level and lead to nonclassical light fields has been a central
objective in quantum optics for many years. After this has been achieved in
individual micro-cavities representing an effectively zero-dimensional volume,
this line of research has shifted its focus towards engineering devices where
such strong optical nonlinearities simultaneously occur in extended volumes of
multiple nodes of a network. Recent technological progress in several
experimental platforms now opens the possibility to employ the systems of
strongly interacting photons these give rise to as quantum simulators. Here we
review the recent development and current status of this research direction for
theory and experiment. Addressing both, optical photons interacting with atoms
and microwave photons in networks of superconducting circuits, we focus on
analogue quantum simulations in scenarios where effective photon-photon
interactions exceed dissipative processes in the considered platforms.
