Wearable systems that monitor muscle activity, store data and deliver feedback therapy are the next frontier in personalized medicine and healthcare. However, technical challenges, such as the fabrication of high-performance, energy-efficient sensors and memory modules that are in intimate mechanical contact with soft tissues, in conjunction with controlled delivery of therapeutic agents, limit the wide-scale adoption of such systems. Here, we describe materials, mechanics and designs for multifunctional, wearable-on-the-skin systems that address these challenges via monolithic integration of nanomembranes fabricated with a top-down approach, nanoparticles assembled by bottom-up methods, and stretchable electronics on a tissue-like polymeric substrate. Representative examples of such systems include physiological sensors, non-volatile memory and drug-release actuators. Quantitative analyses of the electronics, mechanics, heat-transfer and drug-diffusion characteristics validate the operation of individual components, thereby enabling system-level multifunctionalities.