Using epitaxy and the misfit strain imposed by an underlying substrate, it is possible to strain dielectric thin films to percent levels—far beyond where they would crack in bulk. Under such strains, the properties of oxides can be dramatically altered. For example, materials that are not ferroelectric or ferromagnetic in their unstrained state can be transmuted into ferroelectrics, ferromagnets, or materials that are both at the same time. Our results show that for thin films, strain is a viable alternative to the traditional method of chemical substitutions for selecting between alternate ground states.