The Ti-Ni-Nb shape memory alloy possesses a wide transformation hysteresis and excellent shape memory properties, so that it is expected to be used for pipe couplings and mechanical fasteners. The engineering significance of widening hysteresis is discussed. Recent advances in the study of this alloy are reviewed, including microstructure, martenstic transformation, mechanical behavior, strain recovery ratio, low temperature thermal capacity and machinability, etc. Future development of this alloy is also discussed.