Currently, various industries are rapidly developing toward digitization and intelligence, resulting in conventional computing systems based on the von Neumann architecture facing challenges such as high-power consumption and limited data processing capabilities. In the post-Moore era, a memristor is a novel nanoelectronic device with resistance switching memory behavior, which provides a new solution for achieving the integration of data storage and computing technology and breaking through the von Neumann bottleneck. The innovation in medical devices not only advances medical science but also profoundly impacts human health. Specifically, the combination of flexible memristors and biosensors has the potential to add remarkable vigor to the research of implantable electronic devices for health monitoring and disease diagnosis, leading to a great revolution in the biomedical fields. In this paper, we systematically review the latest advancements in functional layer materials selection, structural design, device performance optimization, and implantation experiments of flexible memristors. We focus on introducing the potential application of nanoelectronic devices based on flexible memristors in the field of implantable medical devices for health monitoring and disease diagnosis. Then the development bottleneck of implantable medical devices based on flexible memristors and effective solutions is proposed. Finally, we discuss the importance of clarifying the resistance-switching mechanism of flexible memristors, conducting clinical trials of implantable electronic devices, and promoting interdisciplinary integration to advance the application of flexible memristors in implantable medical devices.