Semiconductor nanomembranes are single-crystal sheets with thickness ranging from 5 to 500nm. They are flexible, bondable, and mechanically ultra-compliant. They present a new platform to combine bottom-up and top-down semiconductor processing to fabricate various three-dimensional (3D) nanomechanical architectures, with an unprecedented level of control. The bottom-up part is the self-assembly, via folding, rolling, bending, curling, or other forms of shape change of the nanomembranes, with top-down patterning providing the starting point for these processes. The self-assembly to form 3D structures is driven by elastic strain relaxation. A variety of structures, including tubes, rings, coils, rolled-up “rugs”, and periodic wrinkles, has been made by such self-assembly. Their geometry and unique properties suggest many potential applications. In this review, we describe the design of desired nanostructures based on continuum mechanics modelling, definition and fabrication of 2D strained nanomembranes according to the established design, and release of the 2D strained sheet into a 3D or quasi-3D object. We also describe several materials properties of nanomechanical architectures. We discuss potential applications of nanomembrane technology to implement simple and hybrid functionalities.