Electrospinning has gained wide attention recently in biomedical applications. Electrospun biocompatible scaffolds are well-known for biomedical applications such as drug delivery, wound dressing, and tissue engineering applications. In this review, the synthesis of polymer-based fiber composites using an electrospinning technique is discussed. Formerly, metal particles were then deposited on the surface of electrospun fibers using sputtering technology. Key nanometals for biomedical applications including silver and copper nanoparticles are discussed throughout this review. The formulated scaffolds were found to be suitable candidates for biomedical uses such as antibacterial coatings, surface modification for improving biocompatibility, and tissue engineering. This review briefly mentions the characteristics of the nanostructures while focusing on how nanostructures hold potential for a wide range of biomedical applications.