Multiferroic magnetoelectric (ME) composites are attractive materials for various electrically and magnetically cross-coupled devices. Many studies have been conducted on fundamental understanding, fabrication processes, and applications of ME composite material systems in the last four decades which has brought the technology closer to realization in practical devices. In this article, we present a review of ME composite materials and some notable potential applications based upon their properties. A brief summary is presented on the parameters that influence the performance of ME composites, their coupling structures, fabrications processes, characterization techniques, and perspectives on direct (magnetic to electric) and converse (electric to magnetic) ME devices. Overall, the research on ME composite systems has brought us closer to their deployment.