  The optics of correlated disordered media is a fascinating research topic
emerging at the interface between the physics of waves in complex media and
nanophotonics. Inspired by photonic structures in nature and enabled by
advances in nanofabrication processes, recent investigations have unveiled how
the design of structural correlations down to the subwavelength scale could be
exploited to control the scattering, transport and localization of light in
matter. From optical transparency to superdiffusive light transport to photonic
gaps, the optics of correlated disordered media challenges our physical
intuition and offers new perspectives for applications. This article reviews
the theoretical foundations, state-of-the-art experimental techniques and major
achievements in the study of light interaction with correlated disorder,
covering a wide range of systems -- from short-range correlated photonic
liquids, to L\'evy glasses containing fractal heterogeneities, to hyperuniform
disordered photonic materials. The mechanisms underlying light scattering and
transport phenomena are elucidated on the basis of rigorous theoretical
arguments. We overview the exciting ongoing research on mesoscopic phenomena,
such as transport phase transitions and speckle statistics, and the current
development of disorder engineering for applications such as light-energy
management and visual appearance design. Special efforts are finally made to
identify the main theoretical and experimental challenges to address in the
near future.
