Nanostructured origami is rapidly transitioning from an elegant technique to fabricate exquisite structures to a platform for integrating novel functionality into crystalline nanomembranes. Nanomembranes, with mechanical properties of typical sheets, can be bent, rolled, and twisted, to return to their original shape, while maintaining their single-crystal nature. The field has advanced from semiconductor bilayer microtubes 15 years ago to quite complex 3D kirigami and origami shapes that demonstrate the potential of 3D devices with unique electronic, optoelectronic, or electromagnetic function. (C) 2015 Elsevier Ltd. All rights reserved.