In the last decades, main evolutions in the field of vascular surgery have been correlated to the development of devices allowing more reliable and safe sustainable treatment. First devices that have been proposed were vascular prostheses made of polymeric materials. The second generation of devices was stents made of metals and alloys. The third generation, endografts, associated these both materials. Materials used as vascular and endovascular devices must meet a number of requirements based on dimensional, physical and mechanical criteria. Ideally, they should demonstrate a behavior as close as possible as that of human arteries in terms of mechanical properties such as compliance, long-term durability, and in terms of biological properties such as biocompatibility, luminal surface healing and thrombogenicity. We propose in the present manuscript a review of properties of materials currently used for the construction of vascular and endovascular devices, future challenges in the fields of new materials and scientific approaches and tests to understand and predict the behavior of the next generations of devices.