Over the past two decades, magnetoelectric (ME) composites and their devices have been an important topic of research. Potential applications ranging from low power sensing to high power converters have been investigated. This review, first, begins with a summary of multiferroic materials that work at room temperature. Such ME materials are usually in composites, and their ME effect generated as a product property of magnetostrictive and piezoelectric composite layers. After that, mechanisms, working principles, and applications of ME composites from heterostructural uncooled magnetic sensors, energy harvesters to highly efficient power converters will be discussed. First, the development of ME sensors in terms of materials and structures to enhance their sensitivities and to reduce noise level is reviewed and discussed. Second, the structure of ME-based energy harvesters is discussed and summarized. Third, the development ME gyrators is summarized for power applications, including the current/voltage conversion, power efficiency, power density and figures of merit. Results demonstrate that our ME gyrator has the ability to satisfy the needs of power conversion with superior efficiency (>90%), offering potential uses in power electronic applications.