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Mechanical energy harvesters are needed for diverse applications, including self-powered wireless sensors, structural and human health monitoring systems, and the extraction of energy from ocean waves. We report carbon nanotube yarn harvesters that electrochemically convert tensile or torsional mechanical energy into electrical energy without requiring an external bias voltage. Stretching coiled yarns generated 250 watts per kilogram of peak electrical power when cycled up to 30 hertz, as well as up to 41.2 joules per kilogram of electrical energy per mechanical cycle, when normalized to harvester yarn weight. These energy harvesters were used in the ocean to harvest wave energy, combined with thermally driven artificial muscles to convert temperature fluctuations to electrical energy, sewn into textiles for use as self-powered respiration sensors, and used to power a light-emitting diode and to charge a storage capacitor.