Mimicking porous topography of natural extracellular matrix is advantageous for successful regeneration of damaged tissues or organs. Nanotechnology being one of the most promising and growing technology today shows an extremely huge potential in the field of tissue engineering. Nanofibrous structures that mimic the native extracellular matrix and promote the adhesion of various cells are being developed as tissue-engineered scaffolds for skin, bone, vasculature, heart, cornea, nervous system, and other tissues. A range of novel biocomposite materials has been developed to enhance the bioactive or therapeutic properties of these nanofibrous scaffolds via surface modifications, including the immobilization of functional cell-adhesive ligands and bioactive molecules such as drugs, enzymes, and cytokines. In skin tissue engineering, usage of allogeneic skin is avoided to reestablish physiological continuity and also to address the challenge of curing acute and chronic wounds, which remains as the area of exploration with various biomimetic approaches. Two-dimensional, three-dimensional scaffolds and stem cells are presently used as dermal regeneration templates for the treatment of full-thickness skin defects resulting from injuries and severe burns. The present review elaborates specifically on the fabrication of nanofibrous structured strategies for wound dressings, wound healing, and controlled release of growth factors for skin tissue regeneration.