The hospital of the future will incorporate revolutionary technologies that will transform health care, delivering highly automated, personalized, and customized patient solutions. These advances will lead to lower health costs, improved access to the best treatments, and significantly better health outcomes for individuals and society. 3D printing plays a key role in this revolution, among these approaches; biofabrication is a growing area of interest. This advanced technology promises to produce patient-specific replacement tissue constructs and restore biological function and health in a rapid, tailored manner. As an alternative approach to current bone grafting and permanent implants, biofabrication combines the body’s own regenerative capacity with bioactive factors and biodegradable biomaterials that are formed into the complex shapes required to restore tissue form and function. Not surprisingly, the promise of biofabrication is driving significant research activity as teams progress this new technology toward routine clinical use. This review article discusses some of this important research, outlining many of the processes, materials, and technologies being developed by groups around the globe. Although the end goal is the same, a range of different 3D-printing approaches are being taken: from extrusion-based polymer fabrication with cellular-level resolution to 3D laser-printed constructs. It is crucial to also develop cutting-edge biomaterials that are structured to guide the tissue regeneration process, and develop advanced 3D computer software that will automatically produce the required digital models. Moving forward, by strong engagement between innovative researchers, clinicians, government, and industry, clinical practice may be transformed as we incorporate these advanced technology platforms.