Power supply represents a critical challenge in the development of body-integrated electronic technologies. Although recent research establishes an impressive variety of options in energy storage (batteries and supercapacitors) and generation (triboelectric, piezoelectric, thermoelectric, and photovoltaic devices), the modest electrical performance and/or the absence of soft, biocompatible mechanical properties limit their practical use. The results presented here form the basis of soft, skin-compatible means for efficient photovoltaic generation and high-capacity storage of electrical power using dual-junction, compound semiconductor solar cells and chip-scale, rechargeable lithium-ion batteries, respectively. Miniaturized components, deformable interconnects, optimized array layouts, and dual-composition elastomer substrates, superstrates, and encapsulation layers represent key features. Systematic studies of the materials and mechanics identify optimized designs, including unusual configurations that exploit a folded, multilayer construct to improve the functional density without adversely affecting the soft, stretchable characteristics. System-level examples exploit such technologies in fully wireless sensors for precision skin thermography, with capabilities in continuous data logging and local processing, validated through demonstrations on volunteer subjects in various realistic scenarios.