The demand for biomaterials that promote the repair, replacement, or restoration of hard and soft tissues continues to grow as the population ages. Traditionally, smart biomaterials have been thought as those that respond to stimuli. However, the continuous evolution of the field warrants a fresh look at the concept of smartness of biomaterials. This review presents a redefinition of the term “Smart Biomaterial” and discusses recent advances in and applications of smart biomaterials for hard tissue restoration and regeneration. To clarify the use of the term “smart biomaterials”, we propose four degrees of smartness according to the level of interaction of the biomaterials with the bio-environment and the biological/cellular responses they elicit, defining these materials as inert, active, responsive, and autonomous. Then, we present an up-to-date survey of applications of smart biomaterials for hard tissues, based on the materials’ responses (external and internal stimuli) and their use as immune-modulatory biomaterials. Finally, we discuss the limitations and obstacles to the translation from basic research (bench) to clinical utilization that is required for the development of clinically relevant applications of these technologies.