The proposal and development of topological photonics have provided a new approach to fundamentally addressing the susceptibility of traditional photonic devices to defects or disorders,significantly enhancing the transmission efficiency and robustness of photonic devices.Among them,non-reciprocal topological photonics which break time-reversal symmetry and support chiral topological states are crucial branches of topological photonics.Their topological properties are characterized by non-zero Chern numbers in two dimensions or topological Chern vectors in three dimensions,exhibiting a rigorous and complete topological protection beyond that of reciprocal topological photonics.This review focuses on introducing the remarkable achievements of non-reciprocal topological photonics in exploring novel physical phenomena(chiral/antichiral edge/surface states,two-dimensional/three-dimensional photonic Chern insulators,magnetic Weyl photonics crystals,etc.)and constructing non-reciprocal robust topological photonic devices(unidirectional waveguides,broadband slow-light delay lines,arbitrarily shaped topological lasers,high-orbital-angular-momentum coherent light sources,etc.).Finally,the present status,potential challenges,and possible breakthroughs in the development of non-reciprocal topological photonics are discussed.