Advances in biofabrication, stem cell biology, and biomaterials engineering have enabled the generation of multicellular tissue constructs capable of recapitulating key aspects of biological function. Despite these advances, the transition from millimeter-scale engineered tissues to centimeter-scale solid organs remains limited by the inability to establish dense, functional vascular networks capable of sustaining metabolically active tissues. This focused review summarizes the complexities involved in generating physiological vasculature and highlights progress in several approaches developed over the past two decades. We discuss progress across several core technology categories, including organoid-based and microfluidic-based platforms to model the vasculatures, as well as the techniques feasible to construct an organ-scale tissue, including recellularization of decellularized organ scaffolds, and bottom-up biofabrication approaches for complex 3D vasculature and high-cell density compatibility. By synthesizing insights from these complementary approaches, we highlight emerging design principles for constructing hierarchical and functional vascular networks. Finally, we outline a forward-looking roadmap toward scalable vascularization strategies that may enable the realization of biofabricated, functional human organs in the coming decade.