Cardiovascular disease is the leading cause of death worldwide, with this trend predicted to continue for the foreseeable future. Common disorders are associated with the stenosis or occlusion of blood vessels. The preferred treatment for the long-term revascularization of occluded vessels is surgery utilizing vascular grafts, such as coronary artery bypass grafting and peripheral artery bypass grafting. Currently, autologous vessels such as the saphenous vein and internal thoracic artery represent the gold standard grafts for small-diameter vessels (<6 mm), outperforming synthetic alternatives. However, these vessels are of limited availability, require invasive harvest, and are often unsuitable for use. To address this, the development of a tissue-engineered vascular graft (TEVG) has been rigorously pursued. This article reviews the current state of the art of TEVGs. The various approaches being explored to generate TEVGs are described, including scaffold-based methods (using synthetic and natural polymers), the use of decellularized natural matrices, and tissue self-assembly processes, with the results of various in vivo studies, including clinical trials, highlighted. A discussion of the key areas for further investigation, including graft cell source, mechanical properties, hemodynamics, integration, and assessment in animal models, is then presented.