Stacking thin polymer films supporting metal nanowire gratings provides a simple route, demonstrated here, to producing large-area metallic woodpile structures with high throughput. Under appropriate conditions the grating films can spontaneously roll up, giving a rapid and controllable method of creating multilayers. The resulting three-dimensional (3D) wire structures are flexible and potentially stretchable. Since this process can be extended to include a wide variety of functional materials, it opens up the manufacture of many tailored 3D optical metamaterials.