Nanofibers exist widely in human tissue with different patterns. Electrospinning nanotechnology has recently gained a new impetus due to the introduction of the concept of biomimetic nanofibers for tissue regeneration. The advanced electrospinning technique is a promising method to fabricate a controllable continuous nanofiber scaffold similar to the natural extracellular matrix. Thus, the biomedical field has become a significant possible application field of electrospun fibers. Although electrospinning has developed rapidly over the past few years, electrospun nanofibers are still at a premature research stage. Further comprehensive and deep studies on electrospun nanofibers are essential for promoting their biomedical applications. Current electrospun fiber materials include natural polymers, synthetic polymers and inorganic substances. This review briefly describes several typically electrospun nanofiber materials or composites that have great potential for tissue regeneration, and describes their fabrication, advantages, drawbacks and future prospects.