To successfully engineer large-sized tissues, establishing vascular structures is essential for providing oxygen, nutrients, growth factors and cells to prevent necrosis at the core of the tissue. The diameter scale of the biofabricated vasculatures should range from 100 to 1,000 µm to support the mm-size tissue while being controllably aligned and spaced within the diffusion limit of oxygen. In this review, insights regarding biofabrication considerations and techniques for engineered blood vessels will be presented. Initially, polymers of natural and synthetic origins can be selected, modified, and combined with each other to support maturation of vascular tissue while also being biocompatible. After they are shaped into scaffold structures by different fabrication techniques, surface properties such as physical topography, stiffness, and surface chemistry play a major role in the endothelialization process after transplantation. Furthermore, biological cues such as growth factors (GFs) and endothelial cells (ECs) can be incorporated into the fabricated structures. As variously reported, fabrication techniques, especially 3D printing by extrusion and 3D printing by photopolymerization, allow the construction of vessels at a high resolution with diameters in the desired range. Strategies to fabricate of stable tubular structures with defined channels will also be discussed. This paper provides an overview of the many advances in blood vessel engineering and combinations of different fabrication techniques up to the present time.