Nanotechnology assists in the development of biocomposite nanofibrous scaffolds that can react positively to changes in the immediate cellular environment and stimulate specific regenerative events at molecular level to generate healthy tissues. Recently, electrospinning has gained huge momentum with greater accessibility of fabrication of composite, controlled and oriented nanofibers with sufficient porosity required for effective tissue regeneration. Current developments include the fabrication of nanofibrous scaffolds which can provide chemical, mechanical and biological signals to respond to the environmental stimuli. These nanofibers are fabricated by simple coating, blending of polymers/bioactive molecules or by surface modification methods. For obtaining optimized surface functionality, with specially designed architectures for the nanofibers (multi-layered, core-shell, aligned), electrospinning process has been modified and simultaneous 'electrospin-electrospraying' process is one of the most lately introduced technique in this perspective. Properties such as porosity, biodegradation and mechanical properties of composite electrospun nanofibers along with their utilization for nerve, cardiac, bone, skin, vascular and cartilage tissue engineering are discussed in this review. In order to locally deliver electrical stimulus and provide a physical template for cell proliferations, and to gain an external control on the level and duration of stimulation, electrically conducting polymeric nanofibers are also fabricated by electrospinning. Electrospun polypyrrole (PPy) and polyaniline (PAN) based scaffolds are the most extensively studied composite substrates for nerve and cardiac tissue engineering with or without electrical stimulations, and are discussed here. However, the major focus of ongoing and future research in regenerative medicine is to effectively exploit the pluripotent potential of Mesenchymal Stem Cell (MSC) differentiation on composite nanofibrous scaffolds for repair of organs.