Bone defects can occur after severe trauma, infection, or bone tumor resection surgery, which requires grafting to repair the defect when it reaches a critical size, as the bone's self-healing ability is insufficient to complete the bone repair. Natural bone grafts or artificial bone grafts, such as bioceramics, are currently used in bone tissue engineering, but the low availability of bone and high cost limit these treatments. Therefore, shape memory polymers (SMPs), which combine biocompatibility, biodegradability, mechanical properties, shape tunability, ease of access, and minimally invasive implantation, have received attention in bone tissue engineering in recent years. Here, we reviewed the various excellent properties of SMPs and their contribution to bone formation in experiments at the cellular and animal levels, respectively, especially for the repair of defects in craniomaxillofacial (CMF) and limb bones, to provide new ideas for the application of these new SMPs in bone tissue engineering.