Tremendous progress of CMOS integrated circuits have been conducted by the down-scaling or the miniaturization of MOSFETs (Metal Oxide Semiconductor Field Effect Transistors). Ten years, ago, the huge direct-tunneling gate leakage current through the thin gate SiO2 film of 1 nm thickness made it impossible to further scale-down the MOSFETs, and replacing the SiO2 by HfO2-based higher-dielectric constant (high-k) material was the solution. In this paper, the history of high-k gate insulator film development and two topics from recent research results regarding ferroelectricity and reliability are described.