Research on the use of biomaterials as vascular substitutes has been dominated in the past by studies focusing on the properties of the materials used. These need to be resistant to protein absorption and should allow cell colonization and integration of the biomaterial within recipient tissue. Despite promising perspectives related both to the appearance of new synthetic materials with biomedical applications and to developments in arterial replacement techniques, there are still many unresolved problems. These include the appearance of occlusive phenomena when using medium- or small-calibre arterial substitutes, and the lack of growth and adaptability of the biomaterial to changes in the host. Notwithstanding, the tissue-engineering techniques developed in recent decades have vastly improved prosthetic behaviour at the blood/biomaterial interface. There is also no doubt that developments in engineered arterial grafts made of natural biomaterials colonized with cells harvested from the recipient patient are drawing us closer and closer to achieving the living graft.