Dacron® (polyethylene terephthalate) and Goretex® (expanded polytetrafluoroethylene) vascular grafts have been very successful in replacing obstructed blood vessels of large and medium diameters. However, as diameters decrease below 6 mm, these grafts are clearly outperformed by transposed autologous veins and, particularly, arteries. With approximately 8 million individuals with peripheral arterial disease, over 500,000 patients diagnosed with end-stage renal disease, and over 250,000 patients per year undergoing coronary bypass in the USA alone, there is a critical clinical need for a functional small-diameter conduit [Lloyd-Jones et al., Circulation 2010;121:e46-e215]. Over the last decade, we have witnessed a dramatic paradigm shift in cardiovascular tissue engineering that has driven the field away from biomaterial-focused approaches and towards more biology-driven strategies. In this article, we review the preclinical and clinical efforts in the quest for a tissue-engineered blood vessel that is free of permanent synthetic scaffolds but has the mechanical strength to become a successful arterial graft. Special emphasis is given to the tissue engineering by self-assembly (TESA) approach, which has been the only one to reach clinical trials for applications under arterial pressure.