This Progress Report reviews recent progress in applying electrospun nanofibers to the emerging field of regenerative medicine. It begins with a brief introduction to electrospinning and nanofibers, with a focus on issues related to the selection of materials, incorporation of bioactive molecules, degradation characteristics, control of mechanical properties, and facilitation of cell infiltration. Next, a number of approaches to fabricate scaffolds from electrospun nanofibers are discussed, including techniques for controlling the alignment of nanofibers and for producing scaffolds with complex architectures. The article also highlights applications of the nanofiber-based scaffolds in four areas of regenerative medicine that involve nerves, dural tissues, tendons, and the tendon-to-bone insertion site. The Progress Report concludes with perspectives on challenges and future directions for design, fabrication, and utilization of scaffolds based on electrospun nanofibers.