The idea of creating replacement for damaged or diseased tissue, which will mimic the physiological conditions and simultaneously promote regeneration by patients' own cells, has been a major challenge in the biomedicine for more than a decade. Therefore, nanofibers are a promising solution to address these challenges. These are solid polymer fibers with nanosized diameter, which show improved properties compared to the materials of larger dimensions or forms and therefore cause different biological responses. On the nanometric level, nanofibers provide a biomimetic environment, on the micrometric scale three-dimensional architecture with the desired surface properties regarding the intended application within the body, while on the macrometric scale mechanical strength and physiological acceptability. In the review, the development of nanofibers as tissue scaffolds, modern wound dressings for chronic wound therapy and drug delivery systems is highlighted. Research substantiates the effectiveness of nanofibers for enhanced tissue regeneration, but ascertains that evidences from clinical studies are currently lacking. Nevertheless, due to the development of nano- and bio-sciences, products on the market can be expected in the near future.