The functionalities of ferroelectrics are closely related to the switchable spontaneous polarization and the polarization-structure coupling. Recent studies have been focused on ferroelectrics that provide additional means to modify the electronic, magnetic, photonic and structural properties. This thesis provides an in-depth study of the coupling of the polarization with other degrees of freedom, based on experimental measurements of the structural changes induced by electric fields and optical excitation. We have studied the mechanism of polarization domains in ferroelectric/dielectric PbTiO3/SrTiO3 superlattices using time-resolved x-ray diffraction. In a superlattice with weakly-coupled component layers, the formation of stripe domains and the non-equal distribution of the polarization have important consequences in the response of the superlattice to applied electric fields. We found that the switching of the stripe domains occurs heterogeneously over the areas under applied electric fields, with a nanosecond timescale. Each component layer, however, responses differently to applied electric fields. The dielectric SrTiO3 layers are less stable and show larger distortion of domains at the early-time regime of switching and a larger piezoelectric expansion at the late-time regime. These observations are commensurate with polarization change due to the elimination of stripe domains. The second component of my thesis focuses on the structural modification of epitaxial multiferroic BiFeO3 thin films. We have found that under electric fields higher than 150 MV/m, the piezoelectricity deviates from its low-field linear response. The increase of the piezoelectricity and a simultaneously increase in the diffuse scattering are consistent with the phonon softening in the proximity of an electric-field-induced phase transition. In addition, a photoinduced strain on the order of 0.5% develops in BiFeO3 thin films within 100 ps under above-bandgap laser pulses. This strain mainly results from the piezoelectric effect due to the screening of the depolarization field in the presence of photoinduced carriers. The relaxation of the strain can be interpreted as a carrier recombination process, which is on the order of 1 ns depending on the film thickness. The widths of Bragg reflections increase under large laser fluence, an effect that can be attributed to strain inhomogeneity.