Vascularization of large bone grafts is one of the main challenges of bone tissue engineering (BTE), and has held back the clinical translation of engineered bone constructs for two decades so far. The ultimate goal of vascularized BTE constructs is to provide a bone environment rich in functional vascular networks to achieve efficient osseointegration and accelerate restoration of function after implantation. To attain both structural and vascular integration of the grafts, a large number of biomaterials, cells, and biological cues have been evaluated. This review will present biological considerations for bone function restoration, contemporary approaches for clinical salvage of large bone defects and their limitations, state-of-the-art research on the development of vascularized bone constructs, and perspectives on evaluating and implementing novel BTE grafts in clinical practice. Success will depend on achieving full graft integration at multiple hierarchical levels, both between the individual graft components as well as between the implanted constructs and their surrounding host tissues. The paradigm of vascularized tissue constructs could not only revolutionize the progress of BTE, but could also be readily applied to other fields in regenerative medicine for the development of new innovative vascularized tissue designs.