This paper is divided into seven main parts. Its purpose is to review the literature to demonstrate the importance of developing bioengineering and global production of biomaterials to care for the level of healthcare in the world. First, the general description of health as a universal human value and assumptions of a long and healthy life policy is presented. The ethical aspects of the mission of medical doctors and dentists were emphasized. The coronavirus, COVID-19, pandemic has had a significant impact on health issues, determining the world’s health situation. The scope of the diseases is given, and specific methods of their prevention are discussed. The next part focuses on bioengineering issues, mainly medical engineering and dental engineering, and the need for doctors to use technical solutions supporting medicine and dentistry, taking into account the current stage Industry 4.0 of the industrial revolution. The concept of Dentistry 4.0 was generally presented, and a general Bioengineering 4.0 approach was suggested. The basics of production management and the quality loop of the product life cycle were analyzed. The general classification of medical devices and biomedical materials necessary for their production was presented. The paper contains an analysis of the synthesis and characterization of biomedical materials supporting medicine and dentistry, emphasizing additive manufacturing methods. Numerous examples of clinical applications supported considerations regarding biomedical materials. The economic conditions for implementing various biomedical materials groups were supported by forecasts for developing global markets for biomaterials, regenerative medicine, and tissue engineering. In the seventh part, recapitulation and final remarks against the background of historical retrospection, it was emphasized that the technological processes of production and processing of biomedical materials and the systematic increase in their global production are a determinant of the implementation of a long and healthy policy.