High permittivity (<em>k</em>) gate dielectric films are widely studied to substitute SiO₂ as gate oxides to suppress the unacceptable gate leakage current when the traditional SiO₂ gate oxide becomes ultrathin. For high-<em>k</em> gate oxides, several material properties are dominantly important. The first one, undoubtedly, is permittivity. It has been well studied by many groups in terms of how to obtain a higher permittivity for popular high-<em>k</em> oxides, like HfO₂ and La₂O₃. The second one is crystallization behavior. Although it’s still under the debate whether an amorphous film is definitely better than ploy-crystallized oxide film as a gate oxide upon considering the crystal boundaries induced leakage current, the crystallization behavior should be well understood for a high-<em>k</em> gate oxide because it could also, to some degree, determine the permittivity of the high-<em>k</em> oxide. Finally, some high-<em>k</em> gate oxides, especially rare earth oxides (like La₂O₃), are not stable in air and very hygroscopic, forming hydroxide. This topic has been well investigated in over the years and significant progresses have been achieved. In this paper, I will intensively review the most recent progresses of the experimental and theoretical studies for preparing higher-<em>k</em> and more stable, in terms of hygroscopic tolerance and crystallization behavior, Hf- and La-based ternary high-<em>k</em> gate oxides.