Clinically, large diameter artery defects (diameter larger than 6 mm) can be substituted by unbiodegradable polymers, such as polytetrafluoroethylene. There are many problems in the construction of small diameter blood vessels (diameter between 1 and 3 mm) and microvessels (diameter less than 1 mm), especially in the establishment of complex vascular models with multi-scale branched networks. Throughout history, the vascularization strategies have been divided into three major groups, including self-generated capillaries from implantation, pre-constructed vascular channels, and three-dimensional (3D) printed cell-laden hydrogels. The first group is based on the spontaneous angiogenesis behaviour of cells in the host tissues, which also lays the foundation of capillary angiogenesis in tissue engineering scaffolds. The second group is to vascularize the polymeric vessels (or scaffolds) with endothelial cells. It is hoped that the pre-constructed vessels can be connected with the vascular networks of host tissues with rapid blood perfusion. With the development of bioprinting technologies, various fabrication methods have been achieved to build hierarchical vascular networks with high-precision 3D control. In this review, the latest advances in 3D bioprinting of vascularized tissues/organs are discussed, including new printing techniques and researches on bioinks for promoting angiogenesis, especially coaxial printing, freeform reversible embedded in suspended hydrogel printing, and acoustic assisted printing technologies, and freeform reversible embedded in suspended hydrogel (flash) technology.