The field of tissue engineering has advanced over the past decade, but the largest impact on human health should be achieved with the transition of engineered solid organs to the clinic. The number of patients suffering from solid organ disease continues to increase, with over 100 000 patients on the U.S. national waitlist and approximately 730 000 deaths in the United States resulting from end-stage organ disease annually. While flat, tubular, and hollow nontubular engineered organs have already been implanted in patients, in vitro formation of a fully functional solid organ at a translatable scale has not yet been achieved. Thus, one major goal is to bioengineer complex, solid organs for transplantation, composed of patient-specific cells. Among the myriad of approaches attempted to engineer solid organs, 3D bioprinting offers unmatched potential. This review highlights the structural complexity which must be engineered at nano-, micro-, and mesostructural scales to enable organ function. We showcase key advances in bioprinting solid organs with complex vascular networks and functioning microstructures, advances in biomaterials science that have enabled this progress, the regulatory hurdles the field has yet to overcome, and cutting edge technologies that bring us closer to the promise of engineered solid organs.