Flexible electronics incorporate all the functional attributes of conventional rigid electronics in formats that have been altered to survive mechanical deformations. Understanding the evolution of device performance during bending, stretching, or other mechanical cycling is, therefore, fundamental to research efforts in this area. Here, we review the various classes of flexible electronic devices (including power sources, sensors, circuits and individual components) and describe the basic principles of device mechanics. We then review techniques to characterize the deformation tolerance and durability of these flexible devices, and we catalogue and geometric designs that are intended to optimize electronic systems for maximum flexibility.