  This article reviews recent theoretical and experimental advances in the
fundamental understanding and active control of quantum fluids of light in
nonlinear optical systems. In presence of effective photon-photon interactions
induced by the optical nonlinearity of the medium, a many-photon system can
behave collectively as a quantum fluid with a number of novel features stemming
from its intrinsically non-equilibrium nature. We present a rich variety of
photon hydrodynamical effects that have been recently observed, from the
superfluid flow around a defect at low speeds, to the appearance of a
Mach-Cherenkov cone in a supersonic flow, to the hydrodynamic formation of
topological excitations such as quantized vortices and dark solitons at the
surface of large impenetrable obstacles. While our review is mostly focused on
a class of semiconductor systems that have been extensively studied in recent
years (namely planar semiconductor microcavities in the strong light-matter
coupling regime having cavity polaritons as elementary excitations), the very
concept of quantum fluids of light applies to a broad spectrum of systems,
ranging from bulk nonlinear crystals, to atomic clouds embedded in optical
fibers and cavities, to photonic crystal cavities, to superconducting quantum
circuits based on Josephson junctions. The conclusive part of our article is
devoted to a review of the exciting perspectives to achieve strongly correlated
photon gases. In particular, we present different mechanisms to obtain
efficient photon blockade, we discuss the novel quantum phases that are
expected to appear in arrays of strongly nonlinear cavities, and we point out
the rich phenomenology offered by the implementation of artificial gauge fields
for photons.
