Electronically-enabled wearable systems that monitor physiological activity and electrophysiological activity hold the key to truly personalized medical care outside of the hospital setting. However, fundamental technical challenges exist in achieving medical systems that are comfortable, unobtrusive and fully integrated without external connections to bench top instruments. In particular, there is a fundamental mismatch in mechanical coupling between existing classes of rigid electronics and soft biological substrates, like the skin. Here we describe new mechanical and electrical design strategies for wearable devices with mechanical properties that approach that of biological tissue. These systems exploit stretchable networks of conformal sensors (i.e. electrodes, temperature sensors, and accelerometers) and associated circuitry (i.e. microcontroller, memory, voltage regulators, rechargeable battery, wireless communication modules) embedded in ultrathin, elastomeric substrates. Quantitative analyses of sensor performance and mechanics under tensile and torsional stresses illustrate the ability to mechanically couple with soft tissues in a way that is mechanically invisible to the user. Representative examples of these soft biointegrated systems can be applied for continuous sensing of muscle and movement activity in the home and ambulatory settings.