This review explores the potential of electrospun nanofibers for drug delivery applications. In the first section, some of the key challenges in drug delivery as well as the promise of electrospun drug loaded nanofibers are highlighted. Techniques of drug incorporation into nanofibers such as blending, surface modification and co-axial electrospinning are detailed. The major requirements of drug eluting scaffolds such as biocompatibility and biodegradability, efficient drug control and release, and adequate mechanical performance are addressed. Drug release kinetics, biodegradability and mechanical properties can be controlled by careful selection of polymers and electrospinning processing parameters while biocompatibility of electrospun mats may be enhanced through surface modification of the nanofibers. The major applications as well as the routes of administration of the drug-loaded electrospun nanostructures are discussed. Currently available drug eluting nanofibrous mats for applications ranging from cancer therapy to wound dressings as well as their preclinical trials are also reviewed.