With increasing interest in nanotechnology, development of nanofibers (n-fibers) by using the technique of electrospinning is gaining new momentum. Among important potential applications of n-fiber-based structures, scaffolds for tissue-engineering represent an advancing front. Nanoscaffolds (n-scaffolds) are closer to natural extracellular matrix (ECM) and its nanoscale fibrous structure. Although the technique of electrospinning is relatively old, various improvements have been made in the last decades to explore the spinning of submicron fibers from biodegradable polymers and to develop also multifunctional drug-releasing and bioactive scaffolds. Various factors can affect the properties of resulting nanostructures that can be classified into three main categories, namely: (1) Substrate related, (2) Apparatus related, and (3) Environment related factors. Developed n-scaffolds were tested for their cytocompatibility using different cell models and were seeded with cells for to develop tissue engineering constructs. Most importantly, studies have looked at the potential of using n-scaffolds for the development of blood vessels. There is a large area ahead for further applications and development of the field. For instance, multifunctional scaffolds that can be used as controlled delivery system do have a potential and have yet to be investigated for engineering of various tissues. So far, in vivo data on n-scaffolds are scarce, but in future reports are expected to emerge. With the convergence of the fields of nanotechnology, drug release and tissue engineering, new solutions could be found for the current limitations of tissue engineering scaffolds, which may enhance their functionality upon in vivo implantation. In this paper electrospinning process, factors affecting it, used polymers, developed n-scaffolds and their characterization are reviewed with focus on application in tissue engineering.