The clinical demand for tissue-engineered vascular grafts is still rising, and there are many challenges that need to be overcome, in particular, to obtain functional small-diameter grafts. The many advances made in cell culture, biomaterials, manufacturing techniques, and tissue engineering methods have led to various promising solutions for vascular graft production, with available options able to recapitulate both biological and mechanical properties of native blood vessels. Due to the rising interest in materials with bioactive potentials, materials from natural sources have also recently gained more attention for vascular tissue engineering, and new strategies have been developed to solve the disadvantages related to their use. In this review, the progress made in tissue-engineered vascular graft production is discussed. We highlight, in particular, the use of natural materials as scaffolds for vascular tissue engineering.