The coupling between magnetic and electric subsystems in composites of ferromagnetic and ferroelectric phases is a product property that is facilitated by mechanical strain that arises due to magnetostriction and the piezoelectric effect in the constituent phases. Such multiferroic composites are of immense interests for studies on the physics of electromagnetic coupling and for use in a variety of applications. Here, we focus on magneto-electric (ME) coupling in nanocomposites. Particular emphasis is on core-shell particles and coaxial fibers, thin film heterostructures, and planar structures with a variety of mechanical connectivity. A brief review of models that predict strong ME effects in nanostructures is followed by synthesis and characterization. Core-shell particulate composites can be prepared by hydrothermal processes and chemical or deoxyribonucleic acid-assisted assembly. Electrospinning techniques have been utilized to prepare defect free core-shell nanofibers. Core-shell particles and fibers can be assembled into superstructures with the aid of magnetic and electric fields and characterized for possible use in advanced technologies. Chemical-vapor deposition techniques have been shown to be effective for the preparation of heterostructures of ferrites and ferroelectrics. Exotic planar multiferroic structures with potential for enhancing ME coupling strengths are also considered. Scanning probe microscopy techniques are ideal for probing the nature of direct- and converse-ME coupling in individual nanostructures. Magnetoelectric characterization of assemblies of nanocomposites can be done by ME voltage coefficient, magnetic field induced polarization, and magneto-dielectric effects. We conclude with a brief discussion on possible avenues for strengthening the product properties in the nanocomposites.