Cardiovascular disease (CVD) affecting blood vessel function is a leading cause of death around the world. A common treatment option to replace the diseased blood vessels is vascular grafting using the patient's own blood vessels. However, patients with CVD are usually lacking vessels for grafting. Recent advances in tissue engineering are now providing alternatives to autologous vascular grafts in the form of tissue-engineered blood vessels (TEBVs). In this review, we will describe the use of different scaffolding systems, cell sources and conditioning approaches for creating fully functional blood vessels. Additionally, we will present the methods used for assessing TEBV functions and describe preclinical and clinical trials for TEBV. Although the early results were encouraging, current designs of TEBV still fall short as a viable clinical option. Implementing the current knowledge in vascular development can lead to improved fabrication and function of TEBV and hasten clinical translation.