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Chiral quantum optics and Topological photonics are both emerging field of research, which have attracted great attention in recent years. Chiral quantum optics provides a new approach to achieve full quantum control of light-matter interaction in a novel manner, which has potential possibility for the implementation of complex quantum information networks. Meanwhile, topological photonics provides a novel route for designing and realizing optical device with unprecedented functionality, such as robust light propagation, the immunity to various structural imperfection, back-scattering suppression as well as unidirectional transmission. The application of topological photonics in chiral quantum optics will promote the whole performance of integrated quantum device with topological protection. In this review, we summarize the progress of chiral quantum optics and topological photonics firstly. Then, we mainly focus on the research of topological chiral edge states based on photonic quantum spin-Hall effect and photonic quantum valley-Hall effect. Furthermore, we introduce the recent work of chiral topological quantum interface formed by embedding quantum dot into the interface between two topologically distinct photonic crystal structures. At last, we give short outlook on the future development direction and prospect for application of topological chiral quantum interface.