There are significant challenges in developing deformable devices at the system level that contain integrated, deformable energy storage devices. Here we demonstrate an origami lithium-ion battery that can be deformed at an unprecedented high level, including folding, bending and twisting. Deformability at the system level is enabled using rigid origami, which prescribes a crease pattern such that the materials making the origami pattern do not experience large strain. The origami battery is fabricated through slurry coating of electrodes onto paper current collectors and packaging in standard materials, followed by folding using the Miura pattern. The resulting origami battery achieves significant linear and areal deformability, large twistability and bendability. The strategy described here represents the fusion of the art of origami, materials science and functional energy storage devices, and could provide a paradigm shift for architecture and design of flexible and curvilinear electronics with exceptional mechanical characteristics and functionalities.