Three-dimensional (3D) bioprinting is a family of rapid prototyping technologies, which assemble biomaterials, including cells and bioactive agents, under the control of a computer-aided design model in a layer-by-layer fashion. It has great potential in organ manufacturing areas with the combination of biology, polymers, chemistry, engineering, medicine, and mechanics. At present, 3D bioprinting technologies can be used to successfully print living tissues and organs, including blood vessels, skin, bones, cartilage, kidney, heart, and liver. The unique advantages of 3D bioprinting technologies for organ manufacturing have improved the traditional medical level significantly. In this article, we summarize the latest research progress of polymers in bioartificial organ 3D printing areas. The important characteristics of the printable polymers and the typical 3D bioprinting technologies for several complex bioartificial organs, such as the heart, liver, nerve, and skin, are introduced.