Bioprinting is a rapidly developing technology for the precise design and manufacture of tissues in various biological systems or organs. Coaxial extrusion bioprinting, an emergent branch, has demonstrated a strong potential to enhance bioprinting's engineering versatility. Coaxial bioprinting assists in the fabrication of complex tissue constructs, by enabling concentric deposition of biomaterials. The fabricated tissue constructs started with simple, tubular vasculature but have been substantially developed to integrate complex cell composition and self-assembly, ECM patterning, controlled release, and multi-material gradient profiles. This review article begins with a brief overview of coaxial printing history, followed by an introduction of crucial engineering components. Afterward, we review the recent progress and untapped potential in each specific organ or biological system, and demonstrate how coaxial bioprinting facilitates the creation of tissue constructs. Ultimately, we conclude that this growing technology will contribute significantly to capabilities in the fields of in vitro modeling, pharmaceutical development, and clinical regenerative medicine.