Complex oxide materials can be driven into transient structural configurations using applied electric fields. Structural changes significantly impact the functional properties of these materials, including their piezoelectricity. Piezoelectric materials grown as heteroepitaxial thin films have therefore attracted much attention because the choice of substrate crystal structure significantly affects the film structure, particularly the in-plane lattice parameter. We report the development of methods to study the structure of complex oxide thin-film materials, strained BiFeO3 films and BaTiO3/CaTiO3 superlattice films, and the application of these tools to probe the response of the crystal structure to applied electric fields. The structural studies use laboratory and synchrotron-based x-ray diffraction to probe the static structure of these layers, and include time-resolved synchrotron x-ray microdiffraction to characterize the structural response to applied fields. The study of superlattice thin films composed of alternating layers of BaTiO3 and CaTiO3 focuses on rotations of the oxygen octahedral building blocks of the perovskite structure. By examining the characteristic x-ray reflections produced by the octahedral rotations, we find these rotations are present in n(BaTiO3)/(6-n)(CaTiO3) superlattices for n = (2,3,4). More intense reflections are produced by superlattice compositions with more consecutive CaTiO3 layers. The pattern of octahedral rotations present in the 2(BaTiO3)/4(CaTiO3) composition is only coherent over one superlattice unit in the out of-plane direction, indicating that the octahedral rotations between BaTiO3 layers are suppressed. We also find the response of these rotations to applied electric fields is far larger for fields with durations of on the order of 1 ms than for pulse-durations on the order of hundreds of nanoseconds. The study of strained BiFeO3 thin films probes the electric-field driven structural phase transition from an initial state consisting of M and Ttilt phases, to the tetragonal-like T phase. The application of an electric field increased the fraction of the film in the T phase at the expense of the M and Ttilt phases. An additional fraction of the film is transformed to the T phase during the electric field pulse, reverting to the M phase when the field is removed. Different M phase populations respond differently to applied electric fields.