Bypass or replacement surgery is required in patients with chronic atherosclerotic artery occlusions. In the absence of an autogenous vein, synthetic polytetrafluoroethylene prostheses can be used. However, these prostheses have shown unsatisfactory bypass grafting results in small-diameter arteries less than 6 mm in diameter. In addition, xenogeneic vessels and vascular prostheses made from biopolymers tend to have poor mechanical strength. The development of vascular prostheses to replace small-diameter vessels is therefore necessary because their hemodynamic properties provoke graft thrombosis. This article provides an overview of the biodegradable synthetic polymers that are used for the experimental fabrication of small-diameter vascular prostheses. Information on the physicochemical properties of various biodegradable synthetic polymers is presented, and there is also a discussion of the methods capable of increasing the hemo- and biocompatibility of the synthetic materials. Currently the most studied polymers in vascular tissue engineering are polyhydroxybutyrate, polyglycolic acid, polycaprolactone, polyurethane and their corresponding copolymers. The use of copolymers and hybrid materials makes it possible to combine the desirable properties of different polymers. Among these polymers, the polyurethanes are the most promising for the development of small-diameter vessel engineering since their structure can provide different rates of biodegradation, strength, and elasticity.