Organs-on-chips (OoCs) have significantly advanced biomedical research by precisely reconstructing human microphysiological systems with biomimetic functions. However, achieving greater structural complexity of cell cultures on-chip for enhanced biological mimicry remains a challenge. To overcome these challenges, 3D bioprinting techniques can be used in directly building complex 3D cultures on chips, facilitating the in vitro engineering of organ-level models. Herein, we review the distinctive features of OoCs, along with the technical and biological challenges associated with replicating complex organ structures. We discuss recent bioprinting innovations that simplify the fabrication of OoCs while increasing their architectural complexity, leading to breakthroughs in the field and enabling the investigation of previously inaccessible biological problems. We highlight the challenges for the development of 3D bioprinted OoCs, concluding with a perspective on future directions aimed at facilitating their clinical translation.