This feature article reviews some concepts for forming single-crystalline semiconductor nanoribbons in ‘stretchable’ geometrical configurations with emphasis on the materials and surface chemistries used in their fabrication and the mechanics of their response to applied strains. As implemented with ribbons that have periodic or aperiodic sinusoidal ‘wavy’ or ‘buckled’ shapes and are surface chemically bonded to elastomeric poly(dimethylsiloxane) (PDMS) supports, these concepts enable levels of mechanical stretchability (and compressibility) that exceed, by orders of magnitude, the intrinsic fracture strains in the ribbon materials themselves. These results, in combination with active functional device elements that can be formed on the surfaces of these ‘wavy’ or ‘buckled’ ribbons, represent a class of potentially valuable building blocks for stretchable electronics, with application possibilities in personal or structural health monitors, sensory skins, spherically curved focal plane arrays and other systems that cannot be achieved easily with other approaches.