There have been a large number of recent studies of the growth of Y-Ba-Cu-O thin films, and these studies have employed a variety of substrates and growth techniques. To date, the highest values of Tc and Jc have been found for films grown by sputtering or coevaporation on single-crystal SrTiO3 substrates, which produces a uniaxially-aligned film with the YBa2Cu3Ox c-axis normal to the film plane. Multilayer growth of films on the same substrate produces a triaxially-aligned film (regions of the film have their c-axis parallel to each of the three substrate <100> directions) with lower values of Jc. Growth of films on a variety of other polycrystalline or amorphous substrates produces randomly-oriented polycrystalline films with low Jc. Although single-crystal SrTiO3 thus produces the best results, this substrate material has a number of undesireable characteristics relative to electronic applications, including very high dielectric constant and a high loss tangent at microwave frequencies. Recently, Simon et al. have shown that LaAlO3 could be used as a substrate for YBaCuO film growth. This substrate is essentially a cubic perovskite with a lattice parameter of 0.3792nm (it has a slight rhombohedral distortion at room temperature) and this material exhibits much lower dielectric constant and microwave loss tangents than SrTiO3. It is also interesting from a film growth standpoint since it has a slightly smaller lattice parameter than YBa2Cu3Ox (a=0.382nm, b=c/3=0.389nm), while SrTiO3 is slightly larger (a=0.3905nm).