Triply-periodic minimal surfaces are commonly observed as the spatial nanostructure of a variety of biological systems as well as self-assembled lipid or copolymer systems. In this talk I will explain what these negatively curved surfaces are, and give a variety of examples where they occur in nature. I will focus on the occurrence of these structures in a number of green butterfly species, where the structure acts as a photonic crystal. That is, the green coloration is the result of the nanostructure, not of a green pigment.