Shape memory polymer (SMP) is a kind of material that can sense and respond to the changes of the external environment, and its behavior is similar to the intelligent reflection of life. Electrospinning, as a versatile and feasible technique, has been used to prepare shape memory polymer fibers (SMPFs) and expand their structures. SMPFs show some advanced features and functions in many fields. In this review, we give a comprehensive overview of SMPFs, including materials, fabrication methods, structures, multifunction, and applications. Firstly, the mechanism and characteristics of SMP are introduced. We then discuss the electrospinning method to form various microstructures, like non-woven fibers, core/shell fibers, hollow fibers and oriented fibers. Afterward, the multiple functions of SMPFs are discussed, such as multi-shape memory effect, reversible shape memory effect and remote actuation of composites. We also focus on some typical applications of SMPFs, including biomedical scaffolds, drug carriers, self-healing, smart textiles and sensors, as well as energy harvesting devices. At the end, the challenges and future development directions of SMPFs are proposed.