The realization of levels of stretchability that extend beyond intrinsic limits of bulk materials is of great importance to stretchable electronics. Here we report large-area, three-dimensional nano-architectures that achieve this outcome in materials that offer both insulating and conductive properties. For the elastomer poly(dimethylsiloxane), such geometries enhance the stretchability and fracture strain by ~ 62 % and ~ 225 % over the bulk, unstructured case. The underlying physics involves local rotations of narrow structural elements in the threedimensional network, as identifi ed by mechanical modelling. To demonstrate the applications of three-dimensional poly(dimethylsiloxane), we create a stretchable conductor obtained by fi lling the interstitial regions with liquid metal. This stretchable composite shows extremely high electrical conductivity ( ~ 24,100 S cm − 1 ) even at strains > 200 % , with good cyclic properties and with current-carrying capacities that are suffi cient for interconnects in light-emitting diode systems. Collectively, these concepts provide new design opportunities for stretchable electronics.