By shock compression we can get independent information about high-pressure phase transition, equations of state (EOSs), etc. under ultra-high pressures, even over 1 Tpa, without pressure calibration. We have measured the shock-wave (Hugoniot) data for several kinds of compounds including brittle materials by a high time-resolution streak camera system (inclined-mirror method). We found the phase transitions on Al2O3, Zro(2), etc., and determined the phase transition points and the EOSs on some oxides, nitrides and chalco-genides. In this report, the Hugoniot results for some topical compounds, ZnS, ZnSe, AlN, Al2O3, ZrO2, are reviewed, the phase transitions and EOSs are discussed. The unresolved problems are also pointed out for the future researches.