The field of tissue engineering is making great strides in developing replacement tissue grafts for clinical use, marked by the rapid development of novel biomaterials, their improved integration with cells, better‐directed growth and differentiation of cells, and improved three‐dimensional tissue mass culturing. One major obstacle that remains, however, is the lack of graft vascularization, which in turn renders many grafts to fail upon clinical application. With that, graft vascularization has turned into one of the holy grails of tissue engineering, and for the majority of tissues, it will be imperative to achieve adequate vascularization if tissue graft implantation is to succeed. Many different approaches have been developed to induce or augment graft vascularization, both in vitro and in vivo. In this review, we highlight the importance of vascularization in tissue engineering and outline various approaches inspired by both biology and engineering to achieve and augment graft vascularization.