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There is increasing interest in materials that combine energy-storing functions with augmented mechanical properties, ranging from flexibility in bending to stretchability to structural properties. In the case of lithium-ion batteries, these mechanical functions could enable their integration in emerging technologies such as wearable, free-form electronics and ultimately as structural elements, for example, in transport applications. This work presents a method to produce flexible LiFePO4 (LFP) electrodes with an extraordinary combination of electrochemical and mechanical performance. Such electrodes exhibit an exceptionally high specific toughness of 1.6 J g-1, combined with superior rate capability (29% increase of the specific capacity at 500 mA g-1, even with 60% reduced conductive additive content) and energy density (60% increase at 500 mA g-1, on an LFP/Li full cell basis), with respect to reference electrodes with typical metallic current collectors. These properties are a result of the strong adhesion of the active material particles to the high surface area carbon nanotube fiber fabric, used as a lightweight, tough, and highly conducting current collector. This strong adherence minimizes electrical resistance, mitigates interfacial failure, and increases ductility through heterogeneous strain after cohesive failure of the inorganic phase. As a result, these electrodes can withstand large deformations before fracture (above 15% tensile deformation), and, even after fracture, they retain excellent electrochemical performance, with a full-electrode-normalized specific capacity of 90 mAh g-1 at 500 mA g-1, approximately double that of unstretched, Al-supported LFP electrodes with equivalent loading.