Topological photonics applies topology, a mathematical study of conserved properties under continuous deformations, to photonics, enabling new theoretical discoveries and applications. Inspired by topological insulators, which allow electrons to flow without dissipation, topological photonics creates interfaces with unique light states. It enables unidirectional waveguides that allow light to flow around imperfections without back-reflection. This review discusses principles and applications in photonic crystals, coupled resonators, metamaterials, and quasicrystals. Key concepts include topology, which characterizes quantized global behavior of wavefunctions. Topological insulators, which conduct on surfaces without dissipation, inspired photonic analogs. The quantum Hall effect, where electrons form quantized orbits, led to photonic analogs. Topological photonics uses carefully designed wave-vector space topologies to create interfaces with useful light states. Topological protection ensures robustness against fabrication imperfections and environmental changes. Edge waveguides, formed by mirrors with different topological invariants, support gapless states. These states are protected by the difference in topological invariants across the interface. Unidirectional waveguides can transmit light around obstacles without reflection, offering robust designs for photonic systems. Topological phases in photonics include Dirac cones, quantum Hall phases, and Weyl points. Gyromagnetic photonic crystals, coupled resonators, and quasicrystals have been used to realize these phases. Topological protection is also observed in bianisotropic metamaterials and 3D systems with line nodes and Weyl points. Applications include photonic circuits less dependent on isolators and slow light insensitive to disorder. Future research aims to discover new topological mirrors, phases, and invariants, and to apply topological concepts to other bosonic systems like surface plasmons and phonons. Technologically, topological effects could improve the robustness of photonic devices against imperfections, enabling more efficient and reliable systems.Topological photonics applies topology, a mathematical study of conserved properties under continuous deformations, to photonics, enabling new theoretical discoveries and applications. Inspired by topological insulators, which allow electrons to flow without dissipation, topological photonics creates interfaces with unique light states. It enables unidirectional waveguides that allow light to flow around imperfections without back-reflection. This review discusses principles and applications in photonic crystals, coupled resonators, metamaterials, and quasicrystals. Key concepts include topology, which characterizes quantized global behavior of wavefunctions. Topological insulators, which conduct on surfaces without dissipation, inspired photonic analogs. The quantum Hall effect, where electrons form quantized orbits, led to photonic analogs. Topological photonics uses carefully designed wave-vector space topologies to create interfaces with useful light states. Topological protection ensures robustness against fabrication imperfections and environmental changes. Edge waveguides, formed by mirrors with different topological invariants, support gapless states. These states are protected by the difference in topological invariants across the interface. Unidirectional waveguides can transmit light around obstacles without reflection, offering robust designs for photonic systems. Topological phases in photonics include Dirac cones, quantum Hall phases, and Weyl points. Gyromagnetic photonic crystals, coupled resonators, and quasicrystals have been used to realize these phases. Topological protection is also observed in bianisotropic metamaterials and 3D systems with line nodes and Weyl points. Applications include photonic circuits less dependent on isolators and slow light insensitive to disorder. Future research aims to discover new topological mirrors, phases, and invariants, and to apply topological concepts to other bosonic systems like surface plasmons and phonons. Technologically, topological effects could improve the robustness of photonic devices against imperfections, enabling more efficient and reliable systems.