Magnetoelectric (ME) materials are attracting increasing attention due to the achievable reading/writing source (electric field and magnetic field in most cases), fast response time, and larger storage density. Therefore, nanocomposites featuring both magnetostriction and piezoelectricity were investigated to increase the converse magnetoelectric (CME, α) coefficient. Among all the nanocomposites, vertically/horizontally-integrated heterostructures were investigated; these materials offer intimate lattice contact, lower clamping effect, dramatically enhanced α, easier reading direction, and the potential to be patterned for complicated applications. In the present work, we focused on three principal goals: (a) creating two-phase vertically integrated heterostructures with different ME materials that provide much larger α, and enhanced strain-induced magnetic shape anisotropy compared with the single-phased ME nanomaterials; (b) creating a vertically integrated heterostructure with large α, lower loss, and higher efficiency; and (c) investigating the stable magnetization states that this heterostructure could achieve, and how it can be used in advanced memory devices and logic devices. Firstly, a BiFeO3-CoFe2O4 (BFO-CFO) heterostructure was epitaxially deposited on Pb(Mg1/3Nb2/3) O3-x at%PbTiO3 (PMN-xPT). The resulting PMN-xPT was proven to have a large piezoelectric effect capable of boosting the CME in the heterostructure to create a much higher α. Secondly, a novel material, CuFe2O4 (CuFO), featuring lower coercivity and loss, was chosen to be self-assembled with BFO. This low-loss could increase the efficiency of the ME effect. Also, our findings revealed a much larger α in the vertically integrated heterostructure compared to single-layer CuFO. Accordingly, the self-assembled structure represents a convenient method for increasing the CME in multiferroic materials. Thirdly, the magnetization states for all these vertically integrated heterostructures were studied. Note that vertically integrated heterostructures are typically fabricated using materials with volatile properties. However, these composites have shown a non-volatile nature with a multi-states (N≥4), which is favored for multiple applications such as multi-level-cell. Moreover, several self-assembled heterostructures were created that are conducive to magnetic anisotropy/coercivity manipulation. One such example is Ni0.65Zn0.35Al0.8Fe1.2O4 (NZAFO) with BFO, which forms a self-assembled nanobelt heterostructure that exhibits high induced magnetic shape anisotropy, and is capable of manipulating magnetic coercivity (from 2 Oe to 50 Oe) and magnetic anisotropy directions (both in-plane and out-of-plane). Finally, we deposited a SrRuO3-CoFe2O4 (SRO-CFO) vertically integrated composite thin film on the single crystal substrate PMN-30PT, with a CFO nanopillar and SRO matrix. In such a heterostructure, the SRO would serve as the conductive materials, while CFO offers the insulated property. This unique conductive/insulating heterostructure could be deposited on PMN-PT single crystals, thus mimicking patterned electrodes on the PMN-PT single crystals with enhanced dielectric constant and 33. / Doctor of Philosophy / Multi-ferroic materials, which contain multiple ferroic orders like ferromagnetism/ferroelectricity order, were widely studied nowadays. These orders are coupled together, which could manipulate one order via another one through the coupling. Due to the achievable reading/writing source (electric field and magnetic field in most of the case), fast response time and larger storage density, magnetoelectric (ME) materials aroused most interests to-date. To be used in different applications, such as memory devices and logic devices, a high transfer efficiency, or say a high coupling coefficient, is required. However, single-phase materials have nearly neglectable ME effect. Therefore, a nanocomposite that contents both magnetostriction and piezoelectricity were investigated to increase the converse magnetoelectric (CME, α) coefficient. Amongst all the nanocomposite, a vertically integrated heterostructure was revealed, which has intimate lattice contact, lower clamping effect, dramatically enhancedα, easier reading direction, and potential to be patterned for complicated applications. In this present work, we focused on several different aspects: (a) creating two-phase vertically integrated heterostructure with different ME materials, which provides much larger α, large strain-induced magnetic shape anisotropy comparing with the single-phased ME nanomaterials; (b): creating a vertically integrated heterostructure with large α and lower losses and higher efficiency; (c) investigate the stable magnetization states that this heterostructure could achieve, which shows the potential of being used in advanced memory devices and logic devices. Firstly, in this work, a BiFeO3-CoFe2O4 (BFO-CFO) heterostructure was epitaxially deposited on the Pb(Mg1/3Nb2/3) O3-x at%PbTiO3 (PMN-xPT), which could boost the CME in the heterostructure to create a much higher α. Then, a novel materials CuFe2O4 (CuFO), was chosen to be self-assembled with BFO, which has lower losses and higher efficiency of the ME effect. Secondly, several self-assembled heterostructures were created, such as Ni0.65Zn0.35Al0.8Fe1.2O4 (NZAFO) with BFO, which manipulated the magnetic coercivity (from 2 Oe to 50 Oe) and magnetic anisotropy directions (Both in-plane and out-of-plane). And a heterostructure: SrRuO3 with CFO, created a vertically integrated heterostructure, could be used as patterned electrodes in different applications. Moreover, magnetization states were studied in all these vertically integrated heterostructures. A multi-states (N≥4) was revealed, which was favored by multiple applications such as multi-level-cell or logical devices. Finally, we deposited a SrRuO3-CoFe2O4 (SRO-CFO) vertically integrated composite thin film on the single crystal substrate PMN-30PT, with a CFO nanopillar and SRO matrix. In such a heterostructure, the SRO would serve as the conductive materials, while CFO offers the insulated property. This unique conductive/insulating heterostructure could be deposited on PMN-PT single crystals, thus mimicking patterned electrodes on the PMN-PT single crystals with enhanced dielectric constant and d_33.