Cardiovascular diseases remain the leading cause of mortality worldwide. Although new therapies are actively being developed and used for cardiovascular pathologies, these attempts have not significantly decreased mortality rates. Regenerative medicine has made enormous progress and set promising approaches over the past half-century. However, since autologous (donor-derived) vascular grafts are lacking, an alternative prosthesis must be constructed for cardiovascular disease patients. In vascular tissue manufacturing and regenerative medicine, scientists seek to improve this significant clinical challenge using bio-fabrication techniques combining additive manufacturing, biomaterials science, and advanced cellular biology. In the last few decades, many improvements and changes in various approaches have helped develop bioengineered concepts that reflect native blood vessels’ structure and function. However, numerous challenges must be overcome to clinically translate the next generation of tissue-engineered vascular transplants. This review provides update on the cell sources, scaffold essential for cardiovascular tissue engineering, and tissue engineering approaches as prospective options for curative therapy for blood vessel disease.