Nanofiber scaffolds have emerged as a revolutionary drug delivery platform for promoting wound healing, due to their unique properties, including high surface area, interconnected porosity, excellent breathability, and moisture absorption, as well as their spatial structure which mimics the extracellular matrix. However, the use of nanofibers to achieve controlled drug loading and release still presents many challenges, with ongoing research still exploring how to load drugs onto nanofiber scaffolds without loss of activity and how to control their release in a specific spatiotemporal manner. This comprehensive study systematically reviews the applications and recent advances related to drug-laden nanofiber scaffolds for skin-wound management. First, we introduce commonly used methods for nanofiber preparation, including electrostatic spinning, sol–gel, molecular self-assembly, thermally induced phase separation, and 3D-printing techniques. Next, we summarize the polymers used in the preparation of nanofibers and drug delivery methods utilizing nanofiber scaffolds. We then review the application of drug-loaded nanofiber scaffolds for wound healing, considering the different stages of wound healing in which the drug acts. Finally, we briefly describe stimulus-responsive drug delivery schemes for nanofiber scaffolds, as well as other exciting drug delivery systems.