Laminated magnetoelectric(ME) energy harvesters, with the advantages of miniaturization, flexibility,and diversified functions, have wide application prospects in self-powered monitoring of low-power devices, such as implanted medicine, Internet of Things(IoT), and micro-electromechanical systems(MEMS). The latest research progress in harvesters is reviewed, introducing their magneto-mechano-electric(MME) coupled energy conversion mechanisms. The types and structural features of various high- and low-frequency magnetic energy harvesters and low-frequency hybrid energy harvesters are examined, and their performances are comprehensively compared and analyzed. The potential advantages of high-frequency magnetic energy harvesters in wirelessly powered medical diagnosis and treatment of implanted devices are highlighted. Further, the significant advantages of low-frequency harvesters in self-powered sensing and monitoring of current-carrying IoT devices are indicated. Finally, existing problems and future development directions for harvesting technology are summarized.