Research in stretchable electronics involves fundamental scientific topics relevant to applications with importance in human healthcare. Despite significant progress in active components, routes to mechanically robust construction are lacking. Here, we introduce materials and composite designs for thin, breathable, soft electronics that can adhere strongly to the skin, with the ability to be applied and removed hundreds of times without damaging the devices or the skin, even in regions with substantial topography and coverage of hair. The approach combines thin, ultralow modulus, cellular silicone materials with elastic, strain-limiting fabrics, to yield a compliant but rugged platform for stretchable electronics. Theoretical and experimental studies highlight the mechanics of adhesion and elastic deformation. Demonstrations include cutaneous optical, electrical and radio frequency sensors for measuring hydration state, electrophysiological activity, pulse and cerebral oximetry. Multipoint monitoring of a subject in an advanced driving simulator provides a practical example.