Multiferroic thin-film heterostructures have attracted a great deal of attention due to the increasing demand for novel energy-efficient micro/nano-electronic devices. Both single phase multiferroic materials like BiFeO3 (BFO) thin films, and strain-mediated magnetoelectric (ME) nanocomposites, have the potential to fulfill a number of functional requirements in actual applications—principally, direct control of magnetization by the application of an electric field (E) and vice-versa. From the perspective of material science, however, it is essential to develop a fuller understanding of the complex fabrication-structure-property triangle relationship for these multiferroic thin films. Pulsed laser deposition (PLD) was used in this study to fabricate diverse epitaxial thin film heterostructures on top of single crystal substrates. The crystal structure, phase transition processes (amongst nanodomain distributions, dielectric phases, magnetic spin states, etc.), and various ME-related properties were characterized under different E or temperature environments. Resulting data enabled us to determine the structure-property relationships for a range of multiferroic systems. First, BFO-based heterostructures were studied. Epitaxial BFO thin films were deposited on top of (001)-oriented Pb(Mg1/3Nb2/3)O3-30PbTiO3 (PMN-30PT) single crystal substrates. The strain states of BFO and crystal structural phases were tunable by E applied on the PMN-30PT via both the in-plane and out-of-plane modes. The strain-mediated antiferromagnetic state changes of BFO were also studied using neutron diffraction spectroscopy under E. Then, CoFe2O4(CFO)/tetragonal BFO nanocomposites were successfully fabricated on top of (001)-oriented LaAlO3 single crystal substrates. The surface morphology, crystal structure, magnetic properties, and ME effects were evaluated and compared with CFO/rhombohedral BFO nanocomposites. To enhance the performance of ME heterostructures with PMN-PT substrates, PMN-30PT single crystals with nanograted electrodes were also studied, which evidenced an enhancement in piezoelectric properties and dielectric constant by 36.7% and 38.3%, respectively. X-ray diffraction reciprocal space mapping (RSM) was used to monitor E-induced changes in the apparent symmetry and domain distribution of near-surface regions for the nanograted PMN-30PT crystals. Finally, in order to add antiferroelectric thin films to the family of strain-mediated multiferroic nanocomposites, epitaxial antiferroelectric thin films were prepared. Epitaxial (Pb0.98La0.02)(Zr0.95Ti0.05)O3 (PLZT) thin films were deposited on differently oriented SrTiO3 single crystal substrates. A thickness dependent incommensurate/commensurate antiferroelectric-to-ferroelectric phase transition was identified. The crystal structure, phase transition characteristics and pathways, and energy storage behaviors from room temperature to 250 ℃ were studied, enabling a more systematic understanding of PLZT-based AFE epitaxial thin films. To summarize, a range of epitaxial thin films were prepared using PLD, whose crystal structures and multiferroic properties were related through the strain. Accordingly, properties such as dielectricity, antiferroelectricity, and antiferromagnetism could be adjusted by E. This study sheds further light on the potential for designing desirable strain-mediated multiferroic nano-/micro-devices in the future. / Doctor of Philosophy / As a general definition, the class of materials known as multiferroics possess more than one ferroic order parameter. Multiferroic thin-film heterostructures have attracted a great deal of attention due to the increasing demand for novel energy-efficient micro/nano-electronic devices. Both single phase multiferroic materials like BiFeO3 (BFO) thin films and strain-mediated magnetoelectric (ME) nanocomposites show significant potential for use in next-generation devices due to the fact that one can control magnetic properties via the application of an electric field (E) and vice-versa. From the perspective of material science, however, it is essential to develop a fuller understanding of the complex fabrication-structure-property triangle relationship for these multiferroic thin films. In this study, diverse epitaxial thin film heterostructures were fabricated on top of single crystal substrates. The crystal structure, phase transition processes (amongst nanodomain distributions, dielectric phases, magnetic spin states, etc.), and various ME-related properties were characterized under different E or temperature environments. Resulting data enabled us to determine the structure-property relationships for a range of multiferroic systems. First, BFO-based heterostructures were studied. Epitaxial BFO thin films were deposited on top of (001)-oriented Pb(Mg1/3Nb2/3)O3-30PbTiO3 (PMN-30PT) single crystal substrates. The strain states of BFO and crystal structural phases were tunable by E applied on the PMN-30PT via both the in-plane and out-of-plane modes. The strain-mediated antiferromagnetic state changes of BFO were studied using powerful neutron diffraction spectroscopy under E. Then, CoFe2O4(CFO)/tetragonal BFO nanocomposites were successfully fabricated on top of (001)-oriented LaAlO3 single crystal substrates. The surface morphology, crystal structure, magnetic properties, and ME effects were discussed and compared with CFO/rhombohedral BFO nanocomposites. To enhance the performance of ME heterostructures with PMN-PT substrates, PMN-PT single crystals with nanograted electrodes were also studied, which evidenced an enhancement in piezoelectric properties and dielectric constant by 36.7% and 38.3%, respectively. X-ray diffraction reciprocal space mapping (RSM) technique was used to monitor E-induced changes in the apparent symmetry and domain distribution of near-surface regions for nanograted PMN-PT crystals. Finally, in order to add antiferroelectric thin films to the family of strain-mediated multiferroic nanocomposites, epitaxial antiferroelectric thin films were prepared. Epitaxial (Pb0.98La0.02)(Zr0.95Ti0.05)O3 (PLZT) thin films were deposited on differently oriented SrTiO3 substrates. A thickness dependent incommensurate antiferroelectric-to-ferroelectric phase transition was identified. The crystal structure, phase transition characteristics and pathways, and energy storage behaviors from room temperature to 250 ℃ were studied, enabling a more systematic understanding of PLZT-based AFE epitaxial thin films. To summarize, a range of epitaxial perovskite thin films were prepared, whose crystal structures and multiferroic properties were related through the strain. Accordingly, the properties such as dielectricity, antiferroelectricity, and antiferromagnetism could be adjusted by E. This study sheds further light on the potential for designing desirable strain-mediated multiferroic nano-/micro-devices in the future.