Blood vessels are highly dynamic and complex structures with a variety of physiological functions, including the transport of oxygen, nutrients, and metabolic wastes. Their normal functioning involves the close and coordinated cooperation of a variety of cells. However, adverse internal and external environmental factors can lead to vascular damage and the induction of various vascular diseases, including atherosclerosis and thrombosis. This can have serious consequences for patients, and there is an urgent need for innovative techniques to repair damaged blood vessels. Polyesters have been extensively researched and used in the treatment of vascular disease and repair of blood vessels due to their excellent mechanical properties, adjustable biodegradation time, and excellent biocompatibility. Given the high complexity of vascular tissues, it is still challenging to optimize the utilization of polyesters for repairing damaged blood vessels. Nevertheless, they have considerable potential for vascular tissue engineering in a range of applications. This summary reviews the physicochemical properties of polyhydroxyalkanoate (PHA), polycaprolactone (PCL), poly-lactic acid (PLA), and poly(lactide-co-glycolide) (PLGA), focusing on their unique applications in vascular tissue engineering. Polyesters can be prepared not only as 3D scaffolds to repair damage as an alternative to vascular grafts, but also in various forms such as microspheres, fibrous membranes, and nanoparticles to deliver drugs or bioactive ingredients to damaged vessels. Finally, it is anticipated that further developments in polyesters will occur in the near future, with the potential to facilitate the wider application of these materials in vascular tissue engineering.