Biological materials science is a new and vibrant field of materials science and engineering. Although biologists have been studying organisms for centuries, it is only recently that materials scientists have started to use their fantastic experimental, computational, and analytical arsenal of tools to reveal new features. We present the Arzt heptahedron, which defines seven unique and defining characteristics of biological materials. The plethora of different structures and mechanical properties of biological materials is systematized through a new paradigm: eight structural design elements, which are motifs appearing on different species and scales, and which enable analytical treatment and lead to enhanced understanding. We have applied this approach to approximately twenty different organisms. We illustrate our approach by applying this knowledge to the toucan beak, rabbit and pig skin, fish scales, and feathers. It is fascinating to see that characterization techniques such as optical, transmission and scanning electron, and atomic force microscopy, SAXS, Micro and Nano CT, and mechanical testing techniques such as nanoindentation, tensile and compressive testing are helping us to better understand these complex structures. Current efforts at bioinspired materials and designs are also discussed.