The present research work focuses on the fabrication and characterization of epitaxial heterostructures of 0.7 Pb(Mg1/3N2/3)O3 – 0.3 PbTiO3 (PMN-PT) and La0.6Sr0.4MnO3 (LSMO) using multi target pulsed laser ablation technique. Different heterostructures such as bilayered thin films with different individual layer thickness; symmetric and asymmetric superlattices of different periodicities were fabricated. Roles of individual layer thickness, elastic strain and interfaces between PMN-PT and LSMO layers on different physical properties were studied. An attempt has been made to understand the influence of the charge depleted interface states in addition to the probable strain mediated elastic coupling effect on the observed magneto-dielectric response in these engineered heterostructures. Chapter 1 provides a brief introduction to the multiferroic materials, occurrence of magnetoelectric (ME) coupling in them, their possible technological applications and the challenges involved. A short historical account of the multiferroic research is discussed to emphasize the importance of artificial multiferroics, particularly the engineered thin film heterostructures. Finally the specific objectives of the current research are outlined. Chapter 2 deals with the various experimental studies carried out in this research work. It gives the details of the experimental set up and the basic operation principles of various structural and physical characterizations of the materials prepared. A brief explanation of material fabrication, structural, micro structural and physical property measurements is discussed. Chapter 3 addresses the phase formation, structural and microstructural features of the engineered heterostructures fabricated epitaxially on single crystalline LaAlO3 (100) substrates. A thin layer of LaNiO3 used as the bottom electrode material for electrical characterizations was grown on the bare substrate prior to the fabrication of the PMN-PT/LSMO heterostructures. The structural and microstructural features of different individual layers were also studied by fabricating single layer thin films of the materials. The effects of individual layer thicknesses on the surface roughness, grain size and lattice strain of the heterostructures are discussed. Chapter 4 deals with the ferroelectric studies of the PMN-PT/LSMO epitaxial heterostructures. Polarization hysteresis (P-E), capacitance – voltage (C-V) and pulsed polarization (PUND) measurements were carried out as functions of applied voltage, frequency and delay time to characterize the ferroelectric properties of the heterostructures. All the bilayered heterostructures exhibited robust ferroelectric response and contribution of non – remnant components to their polarization behaviour were observed from the P-E studies. The symmetric superlattices did not exhibit any ferroelectricity due to high leakage current conduction. After optimizing the LSMO and PMN-PT layer thicknesses ferroelectricity was observed in the asymmetric superlattices accompanied by substantial reduction in the leakage current conduction. The P-E loops were found to be asymmetrically shifted along the electric field axis in all the superlattices indicating the presence of dielectric passive layers and strong depolarizing fields at the interfaces between PMN-PT and LSMO. Chapter 5 deals with the ferromagnetic studies of the PMN-PT/LSMO heterostructures. All the heterostructures exhibited ferromagnetic behaviour in the temperature range of 10 K – 300 K with an in plane magnetic easy axis ([100]) compared to the out of plane ([001]) direction. The magnetization behaviour of the bilayers and superlattices as a function of magnetic field strength, temperature and different individual layer thickness of PMN-PT and LSMO are discussed in terms of the oxygen deficiency, magnetic dead layers and lattice strain effects in these engineered epitaxial heterostructures. Chapter 6 addresses the magneto-dielectric response, dielectric properties and ac conduction properties of the engineered biferroic heterostructures. In order to investigate the manifestation of strain mediated ME coupling in these heterostructures their dielectric response as a function of ac electric signal frequency have been studied under different static magnetic fields over a wide range of temperatures. The appearance of magneto-capacitance and its dependence on magnetic field strength and temperature along with the magnetoresistive characteristics of the heterostructures suggested that the charge depleted interfaces between PMN-PT and LSMO can have an effect on the observed dielectric response in addition to the probable strain mediated ME coupling. Dielectric characterization of the heterostructures performed over a wide range of temperature indicated a Maxwell-Wagner type relaxation mechanism. The manifestation of Maxwell-Wagner effect and the very low activation energy of ac conductivity obtained from the ac conduction studies revealed the strong influence of the charge depleted interfaces between PMN-PT and LSMO on the dielectric properties of the heterostructures. Chapter 7 deals with the dc leakage current conduction characteristics of the heterostructures. The leakage current characterization was performed over a wide range of temperature and analyzed in the framework of different models to investigate the leakage mechanism. All the heterostructures were found to obey the power law I∝Vα over the entire range of temperature with different values of α at different applied voltages. The bilayered heterostructures exhibited ohmic conduction in the lower electric field region and space charge limited conduction was observed at higher electric fields. On the other hand the low field dc conduction behaviour of the superlattices could not be attributed unambiguously to a single mechanism. Depending on the superlattice periodicity the low field conduction behaviour was dominated by either Poole-Frenkel (PF) emission or a combined contribution from the PF effect and ohmic conduction. At higher electric fields all the superlattices exhibited space charge limited conduction. Chapter 8 gives the summary and conclusions of the present study and also discusses about the future work that could give more insight into the understanding of the engineered epitaxial biferroic heterostructures.