Hybrid organic-inorganic metal halide perovskite (HOIP)-based memristors have captured strong attention not only as an emerging candidate for next-generation high-density information storage technology but also for use in healthcare technology and the Internet of Things (IoT) because of their unique properties: low weight, flexibility, compatibility, stretchability, and low power consumption. In this Perspective, we review the recent advances of various aspects of flexible memristors focusing on the selection of the flexible substrates, materials, interfaces, several resistive switching mechanisms, and different methodologies of perovskite growth. The current state of the art of the memristor as an artificial synapse, light-induced resistive switching, and logic gates is comprehensively and systematically reviewed. Finally, we briefly discuss the stability factors of perovskites and present the conclusion with a broad outlook on the progress and challenges in the field of perovskite-based flexible memristors.