Twistable and stretchable fiber-based electrochemical devices having high performance are needed for future applications, including emerging wearable electronics. Weavable fiber redox supercapacitors and strain sensors are here introduced, which comprise a dielectric layer sandwiched between functionalized buckled carbon nanotube electrodes. On the macroscopic scale, the sandwiched core rubber of the fiber acts as a dielectric layer for capacitive strain sensing and as an elastomeric substrate that prevents electrical shorting and irreversible structural changes during severe mechanical deformations. On the microscopic scale, the buckled CNT electrodes effectively absorb tensile or shear stresses, providing an essentially constant electrical conductance. Consequently, the sandwich fibers provide the dual functions of (1) strain sensing, by generating approximately 115.7% and 26% capacitance changes during stretching (200%) and giant twist (1700 rad·m–1 or 270 turns·m–1), respectively, and (2) electrochemical energy storage, providing high linear and areal capacitances (2.38 mF·cm–1 and 11.88 mF·cm–2) and retention of more than 95% of initial energy storage capability under large mechanical deformations.