Biomaterials are mostly any natural and synthetic materials which are compatible from a biological point of view with the human body. Biomaterials are widely used to sustain, increase, reestablish or substitute the biological function of any injured tissue and organ from the human body. Additionally, biomaterials are uninterruptedly in contact with the human body, i.e., tissue, blood and biological fluids. For this reason, an essential feature of biomaterials is their biocompatibility. Consequently, this review summarizes the classification of different types of biomaterials based on their origin, as natural and synthetic ones. Moreover, the advanced applications in pharmaceutical and medical domains are highlighted based on the specific mechanical and physical properties of biomaterials, concerning their use. The high-priority challenges in the field of biomaterials are also discussed, especially those regarding the transfer and implementation of valuable scientific results in medical practice.