Cardiovascular disease is a major threat to human health worldwide, and vascular transplantation surgery is a treatment method for this disease. Often, autologous blood vessels cannot meet the needs of surgery. However, allogeneic blood vessels have limited availability or may cause rejection reactions. Therefore, the development of biocompatible artificial blood vessels is needed to solve the problem of donor shortage. Tubular fabrics prepared by textile structures have flexible compliance, which cannot be matched by other structural blood vessels. Therefore, biomedical artificial blood vessels have been widely studied in recent decades up to the present. This article focuses on reviewing four textile methods used, at present, in the manufacture of artificial blood vessels: knitting, weaving, braiding, and electrospinning. The article mainly introduces the particular effects of different structural characteristics possessed by various textile methods on the production of artificial blood vessels, such as compliance, mechanical properties, and pore size. It was concluded that woven blood vessels possess superior mechanical properties and dimensional stability, while the knitted fabrication method facilitates excellent compliance, elasticity, and porosity of blood vessels. Additionally, the study prominently showcases the ease of rebound and compression of braided tubes, as well as the significant biological benefits of electrospinning. Moreover, moderate porosity and good mechanical strength can be achieved by changing the original structural parameters; increasing the floating warp, enlarging the braiding angle, and reducing the fiber fineness and diameter can achieve greater compliance. Furthermore, physical, chemical, or biological methods can be used to further improve the biocompatibility, antibacterial, anti-inflammatory, and endothelialization of blood vessels, thereby improving their functionality. The aim is to provide some guidance for the further development of artificial blood vessels.