Vascularization is among the top challenges that impede the clinical application of engineered tissues. This challenge has spurred tremendous research endeavor, defined as vascular tissue engineering (VTE) in this article, to establish a pre-existing vascular network inside the tissue engineered graft prior to implantation. Ideally, the engineered vasculature can be integrated into the host vasculature via anastomosis to supply nutrient to all cells instantaneously after surgery. Moreover, sufficient vascularization is of great significance in regenerative medicine from many other perspectives. Due to the critical role of vascularization in successful tissue engineering, we aim to provide an up-to-date overview of the fundamentals and VTE strategies in this article, including angiogenic cells, biomaterial/bio-scaffold design and bio-fabrication approaches, along with the reported utility of vascularized tissue complex in regenerative medicine. We will also share our opinion on the future perspective of this field.