This article reviews recent progress in applying electrospun nanofibers to the emerging field of regenerative medicine. We begin 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. We then discuss a number of approaches to fabrication of scaffolds from electrospun nanofibers, including techniques for controlling the alignment of nanofibers and for producing scaffolds with complex architectures. We also highlight 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. We conclude this review with perspectives on challenges and future directions for design, fabrication, and utilization of scaffolds based on electrospun nanofibers.