Cardiovascular-related medical conditions remain a significant cause of death worldwide despite the advent of tissue engineering research more than half a century ago. Although autologous tissue is still the preferred treatment, donor tissue is limited, and there remains a need for tissue-engineered vascular grafts (TEVGs). The production of extensive vascular tissue (>1 cm3) in vitro meets the clinical needs of tissue grafts and biological research applications. The use of TEVGs in human patients remains limited due to issues related to thrombogenesis and stenosis. In addition to the advancement of simple manufacturing methods, the shift of attention to the combination of synthetic polymers and bio-derived materials and cell sources has enabled synergistic combinations of vascular tissue development. This review details the selection of biomaterials, cell sources and relevant clinical trials related to large diameter vascular grafts. Finally, we will discuss the remaining challenges in the tissue engineering field resulting from complex requirements by covering both basic and clinical research from the perspective of material design.