Cardiovascular disease is the leading cause of mortality in the United States. The limited availability of healthy autologous vessels for bypass grafting procedures has led to the fabrication of prosthetic vascular conduits. Synthetic polymeric materials, while providing the appropriate mechanical strength, lack the compliance and biocompatibility that bioresorbable and naturally occurring protein polymers offer. Vascular tissue engineering approaches have emerged in order to meet the challenges of designing a vascular graft with long-term patency. In vitro culture techniques that have been explored with vascular cell seeding of polymeric scaffolds and the use of bioactive polymers for in situ arterial regeneration have yielded promising results. This review describes the development of polymeric materials in various tissue engineering strategies for the improvement in the mechanical and biological performance of an arterial substitute.