Nanofibrous (NF) scaffolds have been exploited in various fields because of the fascinating advantages of nanofibers. NF scaffolds have ultrathin fiber diameter and large surface-volume ratio. Among various methods for NF scaffold fabrication, electrospinning is one of the most preferred ones because it is simple, scalable and versatile in fabrication of nanofibers with a variety of polymers, additives and structures based on its applications. Electrospun NF scaffolds can be prepared from synthetic and natural polymers. Especially, electrospinning generates fibers that are similar to the fibrous structures of extracellular matrix. Therefore, NF scaffolds have great potential for applications in various biomedical fields, including three-dimensional cell and tissue culture, regeneration of tissues, drug delivery to cells and in screening devices. In this paper, current techniques related to fabrication of NF scaffolds and biomedical applications of these scaffolds will be reviewed.