Blood vessels not only transport oxygen and nutrients to each organ, but also play an important role in the regulation of tissue regeneration. Impaired or occluded vessels can result in ischemia, tissue necrosis, or even life-threatening events. Bioengineered vascular grafts have become a promising alternative treatment for damaged or occlusive vessels. Large-scale tubular grafts, which can match arteries, arterioles, and venules, as well as meso- and microscale vasculature to alleviate ischemia or prevascularized engineered tissues, have been developed. In this review, materials and techniques for engineering tubular scaffolds and vasculature at all levels are discussed. Examples of vascularized tissue engineering in bone, peripheral nerves, and the heart are also provided. Finally, the current challenges are discussed and the perspectives on future developments in biofunctional engineered vessels are delineated.