Organ- and tissue-level biological functions are intimately linked to microscale cell-cell interactions and to the overarching tissue architecture. Together, biofabrication and organoid technologies offer the unique potential to engineer multi-scale living constructs, with cellular microenvironments formed by stem cell self-assembled structures embedded in customizable bioprinted geometries. This study introduces the volumetric bioprinting of complex organoid-laden constructs, which capture key functions of the human liver. Volumetric bioprinting via optical tomography shapes organoid-laden gelatin hydrogels into complex centimeter-scale 3D structures in under 20 s. Optically tuned bioresins enable refractive index matching of specific intracellular structures, countering the disruptive impact of cell-mediated light scattering on printing resolution. This layerless, nozzle-free technique poses no harmful mechanical stresses on organoids, resulting in superior viability and morphology preservation post-printing. Bioprinted organoids undergo hepatocytic differentiation showing albumin synthesis, liver-specific enzyme activity, and remarkably acquired native-like polarization. Organoids embedded within low stiffness gelatins (<2 kPa) are bioprinted into mathematically defined lattices with varying degrees of pore network tortuosity, and cultured under perfusion. These structures act as metabolic biofactories in which liver-specific ammonia detoxification can be enhanced by the architectural profile of the constructs. This technology opens up new possibilities for regenerative medicine and personalized drug testing.