The collaborative project investigated innovative photonic and acoustic materials known as "topological materials." The focus was on new topological phases, topological fibres, non-Hermitian effects, and enhanced wave transport efficiency. These advanced materials possess unique boundary modes that enable the transport of energy and signals, unaffected by disorder or imperfections. The study of electromagnetic and acoustic waves is deeply rooted in history, with their applications important in modern day. Recently, a transformation in this field has been driven by discoveries in artificial periodic systems, termed "photonic and phononic crystals," which exhibit wave manipulation properties not found in nature. However, these capabilities are still susceptible to defects and disorder. The CAS and HKUST teams aimed to employ topological concepts to design systems with transport characteristics for light and sound to make use of the full application potential of these materials.