Human bones have unique structures and characteristics, and replacing a natural bone in the case of bone fracture or bone diseases is a very complicated problem. The main goal of this paper was to summarize the recent research on polymer materials as bone substitutes and for bone repair. Bone treatment methods, bone substitute materials as well as their advantages and drawbacks, and manufacturing methods were reviewed. Biopolymers are the most promising materials in the field of artificial bones and using biopolymers with the shape memory effect can improve the integration of an artificial bone into the human body by better mimicking the structure and properties of natural bones, decreasing the invasiveness of surgical procedures by producing deployable implants. It has been shown that the application of the rapid prototyping technology for artificial bones allows the customization of bone substitutes for a patient and the creation of artificial bones with a complex structure.