A major hurdle in the field of tissue engineering and regenerative medicine remains the design and construction of larger (> 1 cm3) in vitro tissues for biological studies and transplantation. While there has been success in creating three-dimensional (3D) capillary networks, relatively large arteries (diameter >3-5 mm), and more recently small arteries (diameter 500 μm-1 mm), there has been no success in the creation of a living dynamic blood vessel network comprising of arterioles (diameter 40-300 μm), capillaries, and venules. Such a network would provide the foundation to supply nutrients and oxygen to all surrounding cells for larger tissues and organs that require a hierarchical vascular supply. In this study, we describe the different technologies and methods that have been employed in an effort to create individual vessels and networks of vessels to support engineered tissues for in vivo and in vitro applications. A special focus is placed on the generation of blood vessels with average dimensions that span from microns (capillaries) to a millimeter (large arterioles). We also identify major challenges while exploring new opportunities to create model systems of the entire vascular tree, including arterioles and venules.