Tissue engineering is an interdisciplinary field of science that has developed very intensively in recent years. The first part of this review describes materials with medical and dental applications from the following groups: metals, polymers, ceramics, and composites. Both positive and negative sides of their application are presented from the point of view of medical application and mechanical properties. A variety of techniques for the manufacture of biomedical components are presented in this review. The main focus of this work is on additive manufacturing and 3D printing, as these modern techniques have been evaluated to be the best methods for the manufacture of medical and dental devices. The second part presents devices for skull bone reconstruction. The materials from which they are made and the possibilities offered by 3D printing in this field are also described. The last part concerns dental transitional implants (scaffolds) for guided bone regeneration, focusing on polylactide–hydroxyapatite nanocomposite due to its unique properties. This section summarises the current knowledge of scaffolds, focusing on the material, mechanical and biological requirements, the effects of these devices on the human body, and their great potential for applications.