Biomaterials are already widely used in medical sciences. The field of biomaterials began to shift to produce materials able to stimulate specific cellular responses at the molecular level. The combined efforts of cell biologists, engineers, materials scientists, mathematicians, geneticists, and clinicians are now used in tissue engineering to restore, maintain, or improve tissue functions or organs. This rapidly expanding approach combines the fields of material sciences and cell biology for the molecular design of polymeric scaffolds with appropriate 3D configuration and biological responses. Future developments for new blood vessels will require improvements in technology of materials and biotechnology together with the increased knowledge of the interactions between materials, blood, and living tissues. Biomaterials represent a crucial mainstay for all these studies.