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Bismuth halogenides, a family of quasi-one-dimensional (1D) materials, including α and α phases of Bi4Br4 and Bi4I4, have been predicted to exhibit rich and interesting topological properties. The single layer of Bi4Br4 was demonstrated to be a quantum spin Hall insulator (QSHI) with a 0.18 eV gap. Such a band gap is large enough for the observation of QSHI at room temperature. Bulk α-Bi4Br4 was categorized as a higher-order topological insulator and was soon examined in experiments. In addition, the α-Bi4Br4 exhibit simultaneously the topological phase and superconductive phase under 3.8–4.3 GPa pressure. While the single layer of Bi4I4 was shown to be close to the critical point of the QSHI/trivial-insulator phase transition, the α-Bi4I4 was considered to be a strong or weak topological insulator. In this work, we reviewed the recent progress in the topological properties of bismuth halogenides, including the theoretical calculations, angle-resolved photoemission spectroscopy, scanned tunneling microscopy analyses, quantum transport measurement and the superconducting phase transfer under pressure. We expect further research of this family material about the non-trivial superconductor and possible Majorana, room-temperature quantum transport effect and potential application in the quantum device for the electronics and information technology.