Topological physics originated from solid state physics and is used to explain the integer Hall conductivity of boundary states in quantum Hall effect. The boundary state realized by topological theory will naturally have some anti-scattering ability in physical principle. Then, by analogy with condensed matter topology, topological theory is applied to photonics, that is, topological photonics is also proposed, which has gradually become an important photonics principle and method. Its novel way of light field regulation has aroused great interest. As an important branch of metaphotonics, topological photonics theory is used in the design of various optical structures. The sub-wavelength artificial optical metamaterials, e.g., photonic crystals and metasurfaces, are applied to propose and realize various novel optical phenomena, including broadband unidirectional propagation and robust transport in microwave or optical band. This paper focuses on topological photonic crystals. According to its development history, the topological physical properties and design methods of photonic crystals based on the optical analogous of topological features such as the effects of quantum Hall, quantum spin Hall and quantum valley Hall are reviewed. Three kinds of topological photonic crystals are introduced, which use symmetry breaking to split degenerate points and open non-trivial band gap. For example, quantum-Hall photonic crystals break time reversal symmetry by using external magnetic field of gyromagnetic crystals. By introducing the coupling of TE and TM modes into bianisotropic media or metal materials, one can realize quantum-spin-Hall photonic crystals with the degeneracy broken of TE and TM modes. Quantum-valley-Hall photonic crystals break the degeneracy of Dirac points by the inversion symmetry broken of the honeycomb lattice. The bulk-edge correspondence in topological theory is explained, and many practical works to realize the robust edge state of topological photonic crystals in theory or experiment are given. Furthermore, the potential applications of topological photonic crystals in micro-nano integrated photonic and quantum optics devices are analyzed, such as robust transport of optical signals, which can still achieve high transmittance under the condition of sharp bending or structural defects. Topological photonic crystals are used to realize various passive devices, such as optical routing, wavelength division multiplexer, optical beam splitter and optical microcavity. Some active devices, e.g. tunable waveguides, optical switches and laser resonators, are also realized by topological photonic crystals. Topological photonic crystals can be used to design quantum optics devices, including quantum light source and two-photon interference device. At the same time, as another important branch of metaphotonics, metasurfaces have also attracted extensive attention. This paper also briefly introduces the important achievements of metasurfaces in micro-optical imaging. In the future, with the further research on physics principles, optoelectronic design, preparation process, package testing and so on in metamaterials, metaphotonics will become an important part of the new generation of information technology and is expected to have a positive and far-reaching impact on the basic and application fields of silicon optoelectronics, integrated circuits, micro-optical technology, micrography, quantum computing, quantum precision measurement, etc.