Due to the prevalence of cardiovascular diseases, there is a large need for small diameter vascular grafts that cannot be fulfilled using autologous vessels. Although medium to large diameter synthetic vessels are in use, no suitable small diameter vascular graft has been developed due to the unique dynamic environment that exists in small vessels. To achieve long term patency, a successful tissue engineered vascular graft would need to closely match the mechanical properties of native tissue, be non-thrombotic and non-immunogenic, and elicit the proper healing response and undergo remodeling to incorporate into the native vasculature. Electrospinning presents a promising approach to the development of a suitable tissue engineered vascular graft. This review provides a comprehensive overview of the different polymers, techniques, and functionalization approaches that have been used to develop an electrospun tissue engineered vascular graft.