Organoids are three-dimensional multicellular models generated through the intrinsic self-organization of stem cells and have emerged as powerful platforms for disease modeling, drug screening, and precision medicine. However, most organoids cultured in vitro lack a functional vascular interface, which restricts oxygen and nutrient transport, leading to central hypoxia and necrosis and ultimately limiting long-term maintenance, maturation, and translational applicability. To address this bottleneck, a range of three-dimensional bioprinting and biofabrication strategies have been developed to support vascularized organoid and organoid-inspired models. Importantly, current technologies do not yet routinely permit the direct fabrication of physiologically complete 1–10 μm capillary beds within organoids. Instead, their major contributions lie in the generation of perfusable mesoscale conduits, endothelialized hollow channels, multicellular architectures, microfluidic perfusion platforms, and self-organizing microenvironments that, together, facilitate vascular integration and maturation. In this review, we summarize the major biofabrication approaches relevant to vascularized organoid models, emphasizing their roles in vascular manufacturing, technical strengths, and limitations. We further discuss material systems specifically relevant to organoid vascular fabrication, including sacrificial materials, endothelialization-supportive matrices, mechanically stable, perfusion-compatible supports, and organ-specific ECM-derived bioinks. In addition, we analyze key vascularization-enabling strategies, such as endothelialized template formation, multicellular bioprinting, dynamic perfusion, microfluidic integration, and self-organization-assisted maturation. By comparing organ-specific requirements across brain, tumor, cardiac, hepatic, renal, pulmonary, pancreatic, and intestinal models, we further highlight how vascular scale, endothelial phenotype, structural hierarchy, and functional endpoints differ by application. Finally, we discuss the major unresolved challenges, particularly the gap between printable mesoscale channels and physiological capillary networks, the mismatch between generic endothelial sources and organ-specific vascular phenotypes, and the lack of standardized functional criteria for evaluating vascularization. Overall, future progress should depend less on direct capillary-scale printing alone and more on integrating biofabrication, perfusion engineering, and developmental self-organization to achieve reproducible, functionally meaningful vascularized organoid models.