Organ shortage is a severe challenge worldwide. Three-dimensional (3D) printing, a rapidly developing engineering and materials science tool, holds considerable promise in generating implantable organ scaffolds that may reduce or eliminate organ shortage. However, translation of 3D printing into clinical therapies has been astonishingly slow and certainly has not matched the pace of technology development. This review outlines challenges and opportunities for the application of 3D printing in tissue and organ regeneration, with emphasis on in vivo applications of 3D-printed scaffolds. Three-dimensional-printed scaffolds for the regeneration of complex tissues and organs, including bone, cartilage, tooth, and skin, serve as prototypes for 3D printing of other tissues and organs such as the liver, kidney, or heart. The aspiration to reduce or eliminate organ shortage appears to hinge on the translation of 3D bioprinting technologies into preclinical studies and clinical trials. The remaining challenges of cell survival, directed differentiation, angiogenesis, and metabolic exchange are far from trial and need to be addressed. Three-dimensional-printed materials will remain a biomaterials and engineering showcase unless applications in preclinical and clinical models are realized. In balance, 3D printing holds considerable promise in regenerative medicine as a unique approach to address organ shortage.