The fact that in vivo the extracellular matrix (ECM) or substratum with which cells interact often includes topography at the nanoscale underscores the importance of investigating cell-substrate interactions and performing cell culture at the submicron scale. An important and exciting direction of research in nanomedicine would be to gain an understanding and exploit the cellular response to nanostructures. Electrospinning is a simple and versatile technique that can produce a macroporous scaffold comprising randomly oriented or aligned nanofibers. It can also accommodate the incorporation of drug delivery function into the fibrous scaffold. Endowed with both topographical and biochemical signals such electrospun nanofibrous scaffolds may provide an optimal microenvironment for the seeded cells. This review covers the analysis and control of the electrospinning process, and describes the types of electrospun fibers fabricated for biomedical applications such as drug delivery and tissue engineering.