Nature provides many biological materials and structures with exceptional energy absorption capabilities. Few, relatively simple molecular building blocks (e.g., calcium carbonate), which have unremarkable intrinsic mechanical properties individually, are used to produce biopolymer-bioceramic composites with unique hierarchical architectures, thus producing biomaterial-architectures with extraordinary mechanical properties. Several biomaterials have inspired the design and manufacture of novel material architectures to address various engineering problems requiring high energy absorption capabilities. For example, the microarchitecture of seashell nacre has inspired multi-material 3D printed architectures that outperform the energy absorption capabilities of monolithic materials. Using the hierarchical architectural features of biological materials, iterative design approaches using simulation and experimentation are advancing the field of bioinspired material design. However, bioinspired architectures are still challenging to manufacture because of the size scale and architectural hierarchical complexity. Notwithstanding, additive manufacturing technologies are advancing rapidly, continually providing researchers improved abilities to fabricate sophisticated bioinspired, hierarchical designs using multiple materials. This review describes the use of additive manufacturing for producing innovative synthetic materials specifically for energy absorption applications inspired by nacre, conch shell, shrimp shell, horns, hooves, and beetle wings. Potential applications include athletic prosthetics, protective head gear, and automobile crush zones.