  Topological photonics is a rapidly emerging field of research in which
geometrical and topological ideas are exploited to design and control the
behavior of light. Drawing inspiration from the discovery of the quantum Hall
effects and topological insulators in condensed matter, recent advances have
shown how to engineer analogous effects also for photons, leading to remarkable
phenomena such as the robust unidirectional propagation of light, which hold
great promise for applications. Thanks to the flexibility and diversity of
photonics systems, this field is also opening up new opportunities to realize
exotic topological models and to probe and exploit topological effects in new
ways. This article reviews experimental and theoretical developments in
topological photonics across a wide range of experimental platforms, including
photonic crystals, waveguides, metamaterials, cavities, optomechanics, silicon
photonics, and circuit QED. A discussion of how changing the dimensionality and
symmetries of photonics systems has allowed for the realization of different
topological phases is offered, and progress in understanding the interplay of
topology with non-Hermitian effects, such as dissipation, is reviewed. As an
exciting perspective, topological photonics can be combined with optical
nonlinearities, leading toward new collective phenomena and novel strongly
correlated states of light, such as an analog of the fractional quantum Hall
effect.
