Though in vivo models provide the most physiologically-relevant environment for studying tissue development and function, an in vitro substitute is being offered by the advancement of three-dimensional (3D) bioprinting technology, which is a reproducible and scalable fabrication strategy providing precise 3D control compared to conventional microfluidic tissue fabrication methods. In this review, vasculature models printed using extrusion-, droplet-, and laser-based bioprinting techniques are summarized and compared. Besides bioprinting of hydrogels as bioinks, an alternative method to obtain vascular models by bioprinting is to use exogenous biomaterial-free cell aggregates such as tissue spheroids and cell pellet, which has also been discussed here. In addition, there have been efforts to fabricate micro-vasculature constructs (e.g., capillaries) to overcome the practical limitations of bioprinting of large scale vascular networks. At the end of the review, limitations and prospective of bioprinting in vasculature modelling has also been expounded.