Reconstructive surgery using autologous vessels is the conventional approach for substitution of diseased vessels or for generation of bypass to improve blood supply downstream of stenosed vessels. In some circumstances the use of autologous material is not possible due to concomitant diseases or previous use, and artificial grafts must be used. Unfortunately, these grafts cannot substitute small-caliber arterial vessels because of thrombotic complications. The objective of tissue engineering at the vascular level is then to generate biological substitutes of arterial conduits with functional characteristics of native vessels, combining cellular components with biodegradable scaffolds. These research projects started in several laboratories, in the late 1990s, and have expanded in different directions using a number of experimental approaches. The objective of this review is to give an overview of the results so far obtained in this area of research, and to discuss the problems related to these investigations, at the experimental and clinical level. The article provides an overview of different biodegradable scaffolds used, experimental techniques for vessels maturation in vitro under mechanical stimulation, and of differentiated as well as precursors of vascular cells, which opens new opportunities for further development of this form of cell transplantation. Finally, the current available results in clinical research will be discussed.