Nanofibers fabrication nowadays has become unimaginable without mentioning or research involving the technique of electrospinning. Due to the vast possibilities that this technique offers in regard to nanofibers morphology, nanofibrous architecture, and application perspective, it has become the main interest of many scientists with various expertise profiles. Electrospun nanofibers are advantageous over conventional fibers due to their lightweight, high surface-to-volume ratio, adjustable fiber diameter/morphology, and well-controlled functionality. This chapter will highlight the possibilities of nanofibers’ functionalization toward nanomedical applications including, drug delivery, wound healing systems, and tissue engineering scaffolds with a focus on bone and nerve tissue repair. The latest studies (from 2017 onwards) are discussed in terms of materials’ composition, fabrication technologies, and significant performance of cultured cells in vitro and most importantly regenerated tissue after implantation in vivo.