Hair-like-diameter superelastic conducting fibers, comprising a buckled carbon nanotube sheath on a rubber core, are fabricated, characterized, and deployed as weavable wires, biosensors, supercapacitors, and strain sensors. These downsized sheath-core fibers provide the demonstrated basis for glucose sensors, supercapacitors, and electrical interconnects whose performance is undegraded by giant strain, as well as ultrafast strain sensors that exploit strain-dependent capacitance changes.