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Abstract 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.