With the increasing demand for wound healing around the world, the level of medical equipment is also increasing, but sutures are still the preferred medical equipment for medical personnel to solve wound closures. Compared with the traditional sutures, the nanofiber sutures produced by combining the preparation technology of drug-eluting sutures have greatly improved both mechanical properties and biological properties. Electrospinning technology has attracted more attention as one of the most convenient and simple methods for preparing functional nanofibers and the related sutures. This review firstly discusses the structural classification of sutures and the performance analysis affecting the manufacture and use of sutures, followed by the discussion and classification of electrospinning technology, and then summarizes the relevant research on absorbable and non-absorbable sutures. Finally, several common polymers and biologically active substances used in creating sutures are concluded, the related applications of sutures are discussed, and the future prospects of electrospinning sutures are suggested.