Technical systems have become more and more complicated in recent decades and require more detailed control of their operation. This primarily relates to the safety, reliability, and efficiency of devices used in medicine, electronics, and other fields. Furthermore, with the development of the conception of the Internet of Things, a lot of attention has been paid to the interaction between humans and high-tech equipment and personal devices. Highly detailed information on the operation of a device or complex system can only be given by a large number of small sensors of different types. As we know, the most sophisticated sensory machine is a living organism. Formerly this thought led to the idea of creating a multisensory platform which would mimic the human skin capabilities. Electronic skin can simultaneously monitor many parameters such as temperature, strain, pressure, magnetic field, and intensity of light; it is also possible to emulate tactile and chemical perception. Nanotechnology serves as a tool for the creation of new sensor materials, and the development of printing technologies supports engineering low-cost, thin, lightweight, transparent, easily deformable, and biocompatible (even transient) electronic devices for monitoring external factors and processing information. In this review we discuss the state-of-the-art and prospects of new materials and technologies towards emerging flexible sensors.