Periodic photonic nanostructures provide a versatile platform to control and engineer light-matter interaction as the photon dispersion in such patterned optical media can be designed to differ significantly from the optical wave dispersion in regular materials. In this chapter, we describe the tunability and robustness of photonic Dirac points (DPs) in plasmonic nanostructures. The tunability of the DP is demonstrated in graphene-based photonic superlattices by adjusting the graphene permittivity via the optical Kerr effect or electrical doping. The robustness of DPs is demonstrated in plasmonic lattices by showing that even very high levels of disorder are unable to localize the modes located near the DP. The robustness of the DP also manifests itself in the fact that the inversely proportional dependence of the transmission on the lattice length near the DP remains unchanged under strong disorder. Additionally, we show the topological properties of photonic nanostructures and their associated topological modes. Zak phases and the existence of topological modes of photonic superlattices consisting of alternating layers of positive- and negative-index materials are related to the signs of the spatial average of their permittivity and permeability, and the polarization of incident light. Finally, we also show that the existence of surface modes is determined by the sign of the spatially averaged permittivity of the plasmonic Bragg fiber composed of nanostructured coaxial cylindrical metal-dielectric multilayers, \( \overline{\varepsilon} \) . Specifically, localized surface modes occur at the interface between the cylindrical core with \( \overline{\varepsilon}<0 \) and the outermost uniform dielectric medium.