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Origami and kirigami, the ancient techniques for making paper works of art, also provide inspiration for routes to structural platforms in engineering applications, including foldable solar panels, retractable roofs, deployable sunshields, and many others. Recent work demonstrates the utility of the methods of origami/kirigami and conceptually related schemes in cutting, folding, and buckling in the construction of devices for emerging classes of technologies, with examples in mechanical/optical metamaterials, stretchable/conformable electronics, micro/nanoscale biosensors, and large‐amplitude actuators. Specific notable progress is in the deployment of functional materials such as single‐crystal silicon, shape memory polymers, energy‐storage materials, and graphene into elaborate 3D micro and nanoscale architectures. This review highlights some of the most important developments in this field, with a focus on routes to assembly that apply across a range of length scales and with advanced materials of relevance to practical applications.

Capabilities for controlled formation of sophisticated 3D micro/nanostructures in advanced materials have foundational implications across a broad range of fields. Recently developed methods use stress release in prestrained elastomeric substrates as a driving force for assembling 3D structures and functional microdevices from 2D precursors. A limitation of this approach is that releasing these structures from their substrate returns them to their original 2D layouts due to the elastic recovery of the constituent materials. Here, a concept in which shape memory polymers serve as a means to achieve freestanding 3D architectures from the same basic approach is introduced, with demonstrated ability to realize lateral dimensions, characteristic feature sizes, and thicknesses as small as ≈500, 10, and 5 µm simultaneously, and the potential to scale to much larger or smaller dimensions. Wireless electronic devices illustrate the capacity to integrate other materials and functional components into these 3D frameworks. Quantitative mechanics modeling and experimental measurements illustrate not only shape fixation but also capabilities that allow for structure recovery and shape programmability, as a form of 4D structural control. These ideas provide opportunities in fields ranging from micro‐electromechanical systems and microrobotics, to smart intravascular stents, tissue scaffolds, and many others.