High permittivity (k) 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-k 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-k 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-k gate oxide because it could also, to some degree, determine the permittivity of the high-k oxide. Finally, some high-k 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-k and more stable, in terms of hygroscopic tolerance and crystallization behavior, Hf- and La-based ternary high-k gate oxides.