This review reports the latest trends in the ceramic composite matrix used for the magnetoelectric (ME) effect. In the last few years, ME composite has become the center of attraction for use in various electrically and magnetically coupled devices. The growth and use of electronic components everywhere have propulsively accelerated the exploration of self-powered electronic and sensor network devices. ME is a feasible technique for addressing difficulties of traditional batteries such as short life span and frequent recharge difficulties. Self-charging multiferroic components have been found for the constant working of mobile electronics that use multiferroic composites in response to magnetoelectric energy transformation. Researchers have rigorously studied the rigid and flexible magnetoelectric composites for their suitability in applications. This paper gives a comparative study between rigid and flexible magnetoelectric composites based on their properties and provides knowledge about the materials for such types of composites. It reviews the latest polymer-based ME materials as well as the related fabrication and polarization methods. The review finally encapsulates the applications in biomedicine, ranging from mechanical energy harvesters to sensors and actuators.