Abstract: The study of topological states is a hot topic in condensed matter physics as it has revealed several new phases of quantum matter. Recently, many theoretical and experimental studies have demonstrated photonic analogues of topological states, based on the fact that these states are a manifestation of one-particle wave behavior, and this has further stimulated research on photonic topological states. Photonic crystals and coupled-resonator arrays provide a flexible platform for simulating topological phases. The purpose of this review is to give a brief introduction to photonic simulations of topological phases in one-dimensional Dirac systems and two-dimensional p-wave superconductors through the design of specific metamaterials, involving band inversion, edge states, domain walls, and zero-energy mode at a vortex, and so forth.