Bending of thin sheets or ribbons is a ubiquitous phenomenon that impacts our daily lives, from the household thermostat to sensors in airbags. At nanometer-scale thicknesses, the mechanics responsible for bending and other distortions in sheets can be employed to create a nanofabrication approach leading to novel nanostructures. The process and resulting structures have been aptly referred to as “nanomechanical architecture.” In this article, we review recent progress in atomistic simulations that not only have helped to reveal the physical mechanisms underlying this nanofabrication approach, but also have made predictions of new nanostructures that can be created. The simulations demonstrate the importance of the atomic structure of the crystalline membrane and of the intrinsic surface stress in governing membrane bending behavior at the nanoscale and making the behavior fundamentally distinct from that at the macroscale. Molecular dynamics simulations of the bending of patterned graphene (a single-atomic layer film) suggest a new method for synthesizing carbon nanotubes with unprecedented control over their size and chirality.