E-field tuning of magnetism has become an exciting new frontier due to its wide range of potential applications in information storage, sensors, and novel electrostatically tunable microwave magnetic devices such as filters, resonators, inductors and phase shifters. Multiferroic composites, consisting of separate ferromagnetic and ferroelectric phases, have been utilized to electrically control magnetic order through strain mediated ME coupling resulting from the inversed electric effect and piezomagnetic effect. In this work, attempts of electrically tuning magnetism were made in nano-composites multiferroics and laminate multiferroic heterostructures. Remarkable Efield control of magnetism in laminate heterostructures was demonstrated, showing a record high E-field induced magnetic anisotropy, towards to realizing large tunable microwave device and spintronic devices. First, we attempt to demonstrate ME coupling in nano-composite multiferroics. One-dimensional multiferroic core (NiFe 2 O 4 ) -shell ( (Pb(Zr 0.52 Ti 0.48 )O 3 ) nanowire was firstly prepared by combining a modified sol-gel process, electrochemical deposition, and subsequent oxidization in anodized nanoporous alumina membranes. Well-defined individual multiferroic core-shell nanowire with clear boundary can be self-assembled under a certain magnetic field and patterned on the template for ME measurement. However, E-field tuning of magnetism in nano-composites is challenge due the large current leakage caused by small resistivity of magnetic phase. In addition, 0-3 type of CoFe 2 O 4 / PZT nano-composite was synthesized by modified Sol-Gel process. The ME coupling was demonstrated through spontaneous electric polarization change as applying a magnetic field. Second, Ni 0.23 Fe 2.77 O 4 (NFO) / PZT (lead zirconium tinatate), Ni 0.26 Zn 0.1 F e 2.63 O 4 (NZFO) / (011) cut PMN-PT, Zn 0 .1Fe 2 .9O 4 (ZFO) / (011) cut PMN-PT, Fe 3 O 4 /PZT, Fe 3 O 4 / (011) cut PMN-PT, and Fe 3 O 4 / (011) cut PZN-PT (lead zinc niobate-lead titanate) were prepared by spin-spray process at a low temperature of 90C. Strong magnetoelectric coupling (ME) and giant microwave tunability were demonstrated by a electrostatic field induced magnetic anisotropic field change in these heterostructures. A high electrostatically tunable ferromagnesim resonance (FMR) field shfit up to 600 Oe, corresponding to a large microwave ME coefficient of 67 Oe cm/kV, was observed in Fe 3 O 4 /PMN-PT heterostructures. A record-high electrostatically tunable FMR field range of 860 Oe with the linewidth of 330 to 380 Oe was demonstrated in Fe 3 O 4 /PZN-PT heterostructure, corresponding to a ME coefficient of 108 Oe cm/kV. Static ME interaction was also investigated and a maximum electric field induced squareness ratio change of 40% was observed in Fe 3 O 4 /PZN-PT. In I would like to express my sincere appreciation and gratitude to my advisor Prof. Nian X. Sun for his constant support, guidance and encouragement in the past four years. Without his support, this dissertation would not have been po...