Electrospinning is a versatile technique for generating a mat of continuous fibers with diameters from a few nanometers to several micrometers. The diversity of electrospinnable materials, and the unique features associated with electrospun fibers make this technique and its resultant structures attractive for applications in the biomedical field. This article presents an overview of this technique focusing on its application for tissue engineering. In particular, the advantages and disadvantages of using an electrospinning mat for biomedical applications are discussed. It reviews the different available electrospinning configurations, detailing how the different process variables and material types determine the obtained fibers characteristics. Then a description of how nanofiber based scaffolds offer great promise in the regeneration or function restoration of damaged or diseased bones, muscles or nervous tissue is reported. Different methods for incorporating active agents on nanofibers and controlling their release mechanisms are also reviewed. The review concludes with some personal perspectives on the future work to be done in order to include electrospinning technique in the industrial development of biomedical materials.