Recently, the rapid development of flexible electronic materials and devices has profoundly influenced various aspects of social development. Flexible magnetoelectric systems (FMESs), leveraging magnetoelectric coupling, hold vast potential applications in the fields of flexible sensing, memory storage, biomedicine, energy harvesting, and soft robotics. Consequently, they have emerged as a significant branch within the realm of flexible electronic devices. According to its working principle, FMES are divided into three categories: FMES based on magnetodeformation and piezoelectric effects, FMES based on giant magnetoresistive effect, and FMES based on electromagnetic induction. Although some articles have reviewed the first two types of FMES, there is a lack of systematic introduction of the FMES based on electromagnetic induction in existing studies, especially the development history and research status of the three types of FMES. Therefore, this paper systematically reviews the development history and research status of these three kinds of FMES and reveals the working principle and mode of the flexible magnetoelectric system from the perspective of the force-electricity-magnetism coupling mode. In addition, the material selection criteria, device manufacturing methods, and application fields of the FMES are also introduced. Finally, this review delves into the challenges and opportunities confronting the development of FMES, exploring the future development directions. This review aims to establish a theoretical foundation and provide methodological strategies for future research on FMES. It is anticipated to promptly address the current gap in this research field and facilitate the development of the flexible electronic family.