For centuries, nanofibers have been fabricated by converting polymeric materials into nanofibers with tunable mixtures, dimensions, pore structure, and interface properties. Nanofibers include many benefits for transporting drug substances with various biomedical applications. Electrospun nanofibers with customizable geometries and release properties are readily formed due to advances in nanotechnology. The structural characteristics of the electrospun nanofibers/nano yarns are tremendous owing to their large surface-to-volume ratio, interconnected pores, lightweight and permeability, which helps in their wide applications in the health care, energy and environmental aspects of research. The present review focuses on the recent advances in electrospun nanofibers for biomedical applications. Further, this review will examine nanofiber uses in therapeutic delivery and tissue engineering. Additionally, the potential biomedical applications of nanofibers in wound healing and cancer research are reviewed.