Electrospun fibers are being studied and developed because they hold considerable promise for realizing some advantages of nanostructured materials. The fibers can be made of biocompatible and biodegradable polymers. Electrospinning has therefore attracted interest in biotechnology and medicine, and there has been rapid growth in this area in recent years. This review presents an introduction to polymer nanofiber electrospinning, focusing on the use of natural proteins and synthetic peptides. We summarize key physical properties of protein-based and peptide-based nanofiber mats, survey biomedical applications of these materials, identify key challenges, and outline future prospects for development of the technology for tissue engineering, drug delivery, wound healing, and biosensors.