Ferroelectric (piezoelectric) and ferromagnetic materials have extensively permeated in modern industry. (Na1/2Bi1/2)TiO3-BaTiO3 (NBT-x%BT) single crystals and K1/2Na1/2NbO3 (KNN) textured ceramics are top environment-friendly candidates which have potential to replace the commercial lead zirconate titanate or PZT. High magnetostrictive strain (up to 400 ppm) of Fe-xat.%Ga makes this alloys promising alternatives to existing magnetostrictive materials, which commonly either contain costly rare-earth elements or have undesirable mechanical properties for device applications. These systems have common characteristics: compositional/thermal/ electrical dependent structural heterogeneity and chemical disorder on sub-micron or nano scale, resulting in diverse local structures and different physical properties. In this work, I have investigated domain and local structures of NBT-x%BT crystals, KNN ceramics and Fe-xat.%Ga alloys under various conditions, mainly by scanning probe and electron transmission techniques. In NBT-x%BT single crystals, polarized light, piezo-response force (PFM) and transmission electron (TEM) microscopies were used to study domain structures and oxygen octahedral tiltings. Hierarchical domain structures were found in NBT: a high-temperature tetragonal ferroelastic domain structure is elastically inherited into a lower temperature rhombohedral ferroelectric phase. Nanoscale domain engineering mechanism was found to still work in NBT-x%BT system and a modified phase diagram was proposed based on domain observations. An increased intensity of octahedral in-phase tilted reflections and a decrease in the anti-phase ones was observed, with increasing x as the morphotropic phase boundary (MPB) is approached. It was also found that Mn substituents favor the formation of long range ordered micro-sized ferroelectric domains and octahedral in-phase tilted regions near the MPB. Nano-size heterogeneous regions were observed within submicron domain structure, indicating that the nanoscale polarization dynamics are not confined by domain boundaries, and the high piezoelectricity of NBT-x%BT is due to a polarization dynamics with high sensitivity to electric field and a broadened relaxation time distribution. In KNN textured ceramics, an aging effect was found to exist in the orthorhombic single phase field, not only in the orthorhombic and tetragonal two-phase field as previously reported. No variation of phase structure was revealed between before and after aging states. However, pronounced changes in domain morphology were observed by both PFM and TEM: more uniform and finer domain structures were then found with aging. These changes were even more pronounced after poling the aged state. A large number of sub-micron lamellar domains within micron-domains were observed: suggesting a domain origin for improved piezoelectric properties. In Fe-xat.%Ga alloys, an underlying inhomogeneity from Ga atoms embedded into the α-Fe matrix was believed to be the origin of giant magneostrictive properties. I have systematically investigated the phase structure and nano-size heterogeneity of Fe-xat.%Ga alloys subjected to different thermal treatments using standard TEM and high resolution TEM for 10<x<30. Nano-precipitates were observed in all specimens studied: A2, D03 and B2 phases were found depending on x. Nano-precipitates of D03 were observed to be dominant for compositions near the magnetostriction peaks in the phase diagram. Quenching was found to increase the volume fraction of nanoprecipitates for x=19, near the first magnetostriction peak. With increasing x to 22.5, nanoprecipitates were observed to undergo a D03 – B2 transformation. A high density of D03 precipitates of nanoscale size was found to be the critical factor for the first maximum in the magnetostriction. / Ph. D.