Because of the unique shape memory effect and superelasticity, equiatomic Ni-Ti alloys have become the most typical shape memory materials in academic research and engineering applications. Numerous investigations have revealed that the martensitic transformation in Ni-Ti alloys could be retarded by incorporating the third element or increasing Ni/Ti ratio, and the characteristics of transformation and shape memory effect could be tailored. The theoretical and experimental studies in recent years indicated that when doping sufficient amounts of defects including excess solute atoms, foreign alloying dopants, vacancies, dislocations and nanosized precipitates into equiatomic Ni-Ti alloys, the resistance from such defects could suppress the first-order martensitic transformation and achieve strain glass transition with the formation of randomly short-range ordered nanodomains. The strain glass transition is characterized by some typical features such as invariant macroscopic structure, appearance of dynamic elastic modulus dip and frequency dispersion in the elastic modulus, broken ergodicity, shape memory effect and unique superelasticity with slim hysteresis over a wide temperature range. In the present paper, the proposition, novel properties and the research progress in the strain glass transition in Ni-Ti based alloys were reviewed. In addition, the principle for designing Ni-Ti based alloys with superelasticity in broad temperature range and their applications in engineering are briefly introduced.