3D bioprinting holds remarkable promise for rapid fabrication of 3D tissue engineering constructs. Given its scalability, reproducibility, and precise multi-dimensional control that traditional fabrication methods do not provide, 3D bioprinting provides a powerful means to address one of the major challenges in tissue engineering: vascularization. Moderate success of current tissue engineering strategies have been attributed to the current inability to fabricate thick tissue engineering constructs that contain endogenous, engineered vasculature or nutrient channels that can integrate with the host tissue. Successful fabrication of a vascularized tissue construct requires synergy between high throughput, high-resolution bioprinting of larger perfusable channels and instructive bioink that promotes angiogenic sprouting and neovascularization. This review aims to cover the recent progress in the field of 3D bioprinting of vascularized tissues. It will cover the methods of bioprinting vascularized constructs, bioink for vascularization, and perspectives on recent innovations in 3D printing and biomaterials for the next generation of 3D bioprinting for vascularized tissue fabrication.