There is great clinical demand for synthetic vascular grafts with improved long-term efficacy. The ideal vascular conduit is easily implanted, nonthrombogenic, biocompatible, resists aneurysmal dilatation, and ultimately degrades or is assimilated as the patient remodels the graft into tissue resembling native vessel. The field of vascular tissue engineering offers an opportunity to design the ideal synthetic graft, and researchers have evaluated a variety of methods and materials for use in graft construction. Electrospinning is one method that has received considerable attention within tissue engineering for constructing so-called tissue scaffolds. Tissue scaffolds are temporary, porous structures which are commonly composed of bioresorbable polymers that promote native tissue ingrowth and have degradation kinetics compatible with a patient's rate of extracellular matrix production in order to successfully transit from synthetic conduits into neovessels. In this review, we summarize the history of tissue-engineered vascular grafts (TEVG), focusing on scaffolds generated by the electrospinning process, and discuss in vivo applications. We review the materials commonly employed in this approach and the preliminary results after implantation in animal models in order to gauge clinical viability of the electrospinning process for TEVG construction. Scientists have studied electrospinning technology for decades, but only recently has it been orthotopically evaluated in animal models such as TEVG. Advantages of electrospun TEVG include ease of construction, favorable cellular interactions, control of scaffold features such as fiber diameter and pore size, and the ability to choose from a variety of polymers possessing a range of mechanical and chemical properties and degradation kinetics. Given its advantages, electrospinning technology merits investigation for use in TEVG, but an emphasis on long-term in vivo evaluation is required before its role in clinical vascular tissue engineering can be realized.