Geometric structures of thin films, prepared and characterized in ultrahigh vacuum, have been determined by dynamical low-energy electron-diffraction analysis. The two systems we have investigated, Pt on Pd(110) and NiO on Ni(100), offer a wide array of interesting structural phenomena, ranging from simple surface relaxation to massive reconstruction of the substrate due to compound formation;The clean surface of Pd(110) is best described by a nonlaterally displaced geometry, which is in sharp contrast to a model proposed by other authors on the basis of their He-atom diffraction evidence for an order-disorder transition at 230 K. Although a residual uncertainty of 0.13A remains, our results clearly do not favor the notion that the atoms of the topmost layer are displaced by 0.7 A along the (001) direction, whether in a correlated fashion or in a random manner;Pt films deposited onto Pd(110) at 105 K retain the (1 x 1) periodicity of the underlying substrate when left unannealed. Auger measurements indicate that film growth at this temperature occurs in a reasonably layer-by-layer manner for at least the first two monolayers. Both one and two-monolayer films exhibit multilayer relaxation characteristic of clean (1 x 1) surfaces of bulk fcc(110) crystals. The magnitude of relaxation is, however, highly dependent on coverage;The (1 x 2) phase of Pt on Pd(110) has an ideal coverage of 2.5 monolayers, and its structure essentially mimics that of the clean surface of bulk Pt(110). The topmost layer is of the missing-row type, the second layer is slightly row paired, and the third layer is significantly rumpled. The overall geometry of the reconstructed film is consistent with a reduction in the large corrugation of the (1 x 2) missing-row structure;NiO(111) on Ni(100) is highly domained, and is sufficiently thick that the substrate does not participate in the diffraction process. The oxide film terminates with a topmost layer of oxygen rather than nickel, and the first interlayer spacing is strongly contracted. The overall geometry of the oxide film is consistent with a reduction in interfacial strain via one-dimensional row matching between the overlayer and substrate.