The human vascular system comprises vessels that carry blood and lymph fluid throughout the body and play a very important role in the sustenance of the physiological homeostasis. Importantly, blood vessels deliver oxygen and nutrients to various organs and in turn remove metabolic wastes from the organs. Due to the current lifestyle modifications as well as increase in geriatric population, there is an increased incidence of vascular diseases due to dysfunction of vascular systems. Auto, allo and xenografts, though clinically used, suffer from their own limitations. Tissue engineered vascular grafts are now being explored. 3D bioprinting, one such scalable, repeatable, and very accurate additive manufacturing technology has the potential to fabricate desired vascular tissues. In this chapter, a brief background on the anatomy and physiology of the vascular tissues is presented, followed by sections on 3D bioprinting and its types. The pros and cons of these methods are also elucidated. The chapter also highlights some of the key works in 4D bioprinting applications and microfluidics-based bioprinting.