Artificial blood vessels composed of viable tissue represent the ideal vascular graft. Compliance, lack of thrombogenicity, and resistance to infections as well as the ability to heal, remodel, contract, and secrete normal blood vessel products are theoretical advantages of such grafts. Three basic elements are generally required for the construction of an artificial vessel: a structural scaffold, made either of collagen or a biodegradable polymer; vascular cells, and a nurturing environment. Mechanical properties of the artificial vessels are enhanced by bioreactors that mimic the in vivo environment of the vascular cells by producing pulsatile flow. Alternative approaches include the production of fibrocollagenous tubes within the recipient's own body (subcutaneous tissue or peritoneal cavity) and the construction of an artificial vessel from acellular native tissues, such as decellularized small intestine submucosa, ureter, and allogeneic or xenogeneic arteries. This review details the most recent developments on vascular tissue engineering, summarizes the results of initial experiments on animals and humans, and outlines the current status and the challenges for the future.