The concept of topology in physics has enabled the understanding of transport and localization properties of materials at their edges based on the properties of their bulk. Originally developed in the context of solid-state physics, the power of this description to unveil novel properties of materials was recognised by the 2016 Nobel prize in physics. The implementation of topological phases of light in photonic lattices has been one of the most active and inspiring areas in optics in the past decade. From a fundamental point of view, the possibility of manipulating the geometry of photonic lattices with currently available micro- and nano-technologies has allowed the exploration of novel topological phases and concepts. Features that are specific to photonic materials such as gain, losses and nonlinearity, or the use of single and entangled photon sources, have permitted the observation of topological phenomena genuine to photonic materials. From the point of view of applications, topological photonics is expected to play an important role in the development of next generation photonic integrated circuits. For instance, topological designs enable the engineering of one way transmission channels in photonic crystals with very efficient transport, even in the presence of sharp bends at the micrometer level.

One of the key aspects in the development of topological transport of light has been the realization of different photonic platforms with specific features. The purpose of this Special Issue of Optical Materials Express is to review the main ones and to show current trends in this field. The issue has 11 articles, both invited and contributed, which include reviews on integrated photonic waveguides (Kremer et al. [1]), lattices of microwave resonators (Reisner et al. [2]), wire-based metamaterials (Yves et al. [3]), photorefractive photonic lattices (Xia et al. [4]), photonic crystals (Iwamoto et al. [5]), microcavity polaritons (Solnyshkov et al. [6]), and quasicrystal lattices (Zilberberg [7]). Those reviews aim at providing in-depth descriptions of specific experimental platforms and perspectives on their use to explore novel phenomena. Two papers discuss the implementation of topological interface modes in lattices of superconducting microwave resonators (Morvan et al. [8] and Huang et al. [9]). Novel geometries to confine photonic modes in topological fibres are discussed by Pilozzi and Conti in [10], and the use of electronic topological insulators to enhance Faraday and Kerr rotation effects is treated by Shah and co-workers in [11]. We hope you find these works inspiring.