With the increasing demand in seamless interface between artificial devices and biological structures, flexible bioelectronics has been developed rapidly in recent years. Compared with traditional rigid bioelectronics, flexible devices are more adaptable to the integration for various parts both inside and outside of the organism. Significant achievements have been made in biomedical devices, neuroelectronics and wearable devices. With the development of flexible bioelectronics, electromagnetics is becoming a crucial part in signal interference reduction and information transmission or feedback, taking advantages of strong penetration and rapid response in a variety of biological materials. In this review, we focus on the latest developments in electromagnetic based flexible bioelectronics, involving materials, sensation, seamless integration, and power supply, as well as the latest achievements in the fields of external wearables, internal implants, soft robotics and drug delivery system. Based on these, the main challenges facing flexible bioelectronics, are analyzed, including stretchability caused by mismatch between mechanical properties of soft and hard components, biocompatibility, environmental stability, to facilitate the further development of flexible bioelectronics.