Purpose Shape memory polymers (SMPs) respond with a change in their shape against a specific stimulus by memorizing their original shape and are reformed after deformation most often by changing the temperature of the surrounding without additional mechanical efforts. In the coming years, these polymers indeed will be in limelight to manufacture textile materials which will retain their shape even after prolonged use under disturbed conditions. This study aims at defining shape memory materials and polymers as well as their technological characteristics and also highlights application in various fields of textiles. Design/methodology/approach The methodology used to explain these SMPs have been carried out starting with the discussion on their properties, their physical nature, types, viz., shape memory alloys (SMAs), shape memory ceramics, shape memory hybrid, magnetic shape memory alloy, shape memory composites, shape memory gels and SMP along with properties of each type. Other related details of these polymers, such as their advantages, structure and mechanism, shape memory functionality, thermally responsive SMPs and applications, have been detailed. Findings It has been observed that the SMPs are very important in the fields of wet and melt-spun fibers to offer novel and functional properties, cotton and wool fabric finishing, to produce SMP films, foams and laminated textiles, water vapor permeable and breathable SMP films, etc. Originality/value The field of SMPs is new, and very limited information is available to enable their smooth production and handling.