Bone, nacre, and other biological materials exhibit unique hierarchical structures at different length scales, and thereby achieve versatile material functions. The excellent performance of bioinspired designs in materials science has attracted the interest of engineers and scientists to expand this bioinspiration to many other materials, including graphene. Among the different designs that draw significant attention, butterfly wings are particularly noteworthy, whose iridescent colors arise from the interaction of light with highly precise multiscale structures that in some cases correspond to a 3D shape of gyroid geometries. Especially, the combination of gyroid designs with graphene can produce mechanical and thermal functions for carbon porous materials that exhibit superior properties such as strength 10 times higher than mild steel, with only around 4.6% the density of this material, featuring also density-insensitive thermal stability, as well as an outstanding impact energy absorption capability as high as 269 MJ/m3. Based on molecular modeling, the physics and mechanics of graphene-based gyroid structures, as well as their performance in the context of thermal conduction and impact energy absorption are included in our current short review.