Flexible devices are emerging as important applications for future display, robotics, in vitro diagnostics, advanced therapies, and energy harvesting. In this review, we provide an overview of recent achievements in flexible mechanical and electrical sensing devices, focusing on the properties and functions of polymeric layers. In the order of historical development, sensing platforms are classified into four types: electronic skins for robotics and medical applications, wearable devices for in vitro diagnostics, implantable devices for human organs or tissues for surgical applications, and advanced sensing devices with additional features such as transparency, self-power, and self-healing. In all of these examples, a polymer layer is used as a versatile component including a flexible structural support and a functional material to generate, transmit, and process mechanical and electrical inputs in various ways. We briefly discuss some outlooks and future challenges toward the next steps for flexible devices.