Electrospinning, a technique well known for fabricating nanoscale fibers, has recently been studied extensively due to its various advantages such as high surface-to-volume ratio, tunable porosity, and ease of surface functionalization. The resulting fibers are extremely useful for applications in the fields of tissue engineering, drug delivery, and wound dressing. Since electrospun fiber mimic extracellular matrix of tissue in terms of scale and morphology, its potential to be used as scaffold is continuously explored by researchers, especially in the field of vascular, nerve, bone, and tendon/ligament tissue engineering. Besides morphology, physical, and chemical properties, electrospun scaffolds are often evaluated through various cell studies. Researchers have adopted approaches such as surface modification and drug loading to enhance the property and function of scaffold. This review gives an overview of some current aspects of various applications of electrospun fibers, particularly in biomedical fields, how researchers have enhanced electrospun fibers with different methods and attempted to overcome the inherent limitation of electrospinning by using novel techniques.