We report classes of electronic systems that achieve thicknesses, effective elastic moduli, bending stiffnesses, and areal mass densities matched to the epidermis. Unlike traditional wafer-based technologies, laminating such devices onto the skin leads to conformal contact and adequate adhesion based on van der Waals interactions alone, in a manner that is mechanically invisible to the user. We describe systems incorporating electrophysiological, temperature, and strain sensors, as well as transistors, light-emitting diodes, photodetectors, radio frequency inductors, capacitors, oscillators, and rectifying diodes. Solar cells and wireless coils provide options for power supply. We used this type of technology to measure electrical activity produced by the heart, brain, and skeletal muscles and show that the resulting data contain sufficient information for an unusual type of computer game controller.