3D printing has the potential for on-demand, patient-specific devices with high structural complexity. However, the tools and biomaterials most widely available for 3D printing are largely limited to fused deposition modelling (FDM) with commodity plastics that lack cell-scale resolution and biological cues. The lack of biologically active materials, also called 'bioinks,' is a key issue that limits the ability to produce engineered tissues, tissue interfaces and functional organs. While advances are being made in the field of biomaterials, current technologies can be combined into hybrid systems that overcome the limitations of a single technique or material, as described in this article.