Bone regeneration is currently one of the most important and challenging tissue engineering approaches in regenerative medicine. Bone regeneration is a promising approach in dentistry and is considered an ideal clinical strategy in treating diseases, injuries, and defects of the maxillofacial region. Advances in tissue engineering have resulted in the development of innovative scaffold designs, complemented by the progress made in cell-based therapies. In vitro bone regeneration can be achieved by the combination of stem cells, scaffolds, and bioactive factors. The biomimetic approach to create an ideal bone substitute provides strategies for developing combined scaffolds composed of adult stem cells with mesenchymal phenotype and different organic biomaterials (such as collagen and hyaluronic acid derivatives) or inorganic biomaterials such as manufactured polymers (polyglycolic acid (PGA), polylactic acid (PLA), and polycaprolactone). This review focuses on different biomaterials currently used in dentistry as scaffolds for bone regeneration in treating bone defects or in surgical techniques, such as sinus lift, horizontal and vertical bone grafts, or socket preservation. Our review would be of particular interest to medical and surgical researchers at the interface of cell biology, materials science, and tissue engineering, as well as industry-related manufacturers and researchers in healthcare, prosthetics, and 3D printing, too.