Nature assembles weak organic and inorganic constituents into sophisticated hierarchical structures, forming structural composites that demonstrate impressive combinations of strength and toughness. Two such composites are the nacre structure forming the inner layer of many mollusk shells, whose brick-and-mortar architecture has been the gold standard for biomimetic composites, and the cuticle forming the arthropod exoskeleton, whose helicoidal fiber-reinforced architecture has only recently attracted interest for structural biomimetics. In this review, we detail recent biomimetic efforts for the fabrication of strong and tough composite materials possessing the brick-and-mortar and helicoidal architectures. Techniques discussed for the fabrication of nacre- and cuticle-mimetic structures include freeze casting, layer-by-layer deposition, spray deposition, magnetically assisted slip casting, fiber-reinforced composite processing, additive manufacturing, and cholesteric self-assembly. Advantages and limitations to these processes are discussed, as well as the future outlook on the biomimetic landscape for structural composite materials.