Although liver transplantation is the gold-standard therapy for end-stage liver disease, the shortage of suitable organs results in only 25% of waitlisted patients undergoing transplants. Three-dimensional (3D) bioprinting is an emerging technology and a potential solution for personalized medicine applications. This review highlights existing 3D bioprinting technologies of liver tissues, current anatomical and physiological limitations to 3D bioprinting of a whole liver, and recent progress bringing this innovation closer to clinical use. We reviewed updated literature across multiple facets in 3D bioprinting, comparing laser, inkjet, and extrusion-based printing modalities, scaffolded versus scaffold-free systems, development of an oxygenated bioreactor, and challenges in establishing long-term viability of hepatic parenchyma and incorporating structurally and functionally robust vasculature and biliary systems. Advancements in liver organoid models have also increased their complexity and utility for liver disease modeling, pharmacologic testing, and regenerative medicine. Recent developments in 3D bioprinting techniques have improved the speed, anatomical, and physiological accuracy, and viability of 3D-bioprinted liver tissues. Optimization focusing on 3D bioprinting of the vascular system and bile duct has improved both the structural and functional accuracy of these models, which will be critical in the successful expansion of 3D-bioprinted liver tissues toward transplantable organs. With further dedicated research, patients with end-stage liver disease may soon be recipients of customized 3D-bioprinted livers, reducing or eliminating the need for immunosuppressive regimens.