Over the past decade magnetoelectric (ME) mutiferroic (MF) materials and their devices are one of the highest priority research topics that has been investigated by the scientific ferroics community to develop the next generation of novel multifunctional materials. These systems show the simultaneous existence of two or more ferroic orders, and cross-coupling between them, such as magnetic spin, polarisation, ferroelastic ordering, and ferrotoroidicity. Based on the type of ordering and coupling, they have drawn increasing interest for a variety of device applications, such as magnetic field sensors, nonvolatile memory elements, ferroelectric photovoltaics, nano-electronics etc. Since single-phase materials exist rarely in nature with strong cross-coupling properties, intensive research activity is being pursued towards the discovery of new single-phase multiferroic materials and the design of new engineered materials with strong magneto-electric (ME) coupling. This review article summarises the development of different kinds of multiferroic material: single-phase and composite ceramic, laminated composite and nanostructured thin films. Thin-film nanostructures have higher magnitude direct ME coupling values and clear evidence of indirect ME coupling compared with bulk materials. Promising ME coupling coefficients have been reported in laminated composite materials in which the signal to noise ratio is good for device fabrication. We describe the possible applications of these materials.