Through the measurement of Hugoniot parameters, we can get useful information about high-pressure phase transitions, equations of state (EOS), etc. of solids, without pressure calibration. And, we can discuss the transition dynamics, because the relaxation times of phase transition and compression process are of the same order. We have performed the Hugoniot-measurement experiments on various kinds of compound materials including oxides, nitrides, borides and chalcogenides by using a high time-resolution streak photographic system combined with the propellant guns. The structure-phase transitions have been observed for several kinds of inorganic materials, TiO2, ZrO2, Gd3Ga5O12, AlN, ZnS, ZnSe, etc. The phase transition pressures under shock and static compressions of metals, ionic materials, semiconductors and some ceramics are consistent with each other. Those are not consistent for strong covalent bonding materials such as C, BN and SiO2. Here, the Hugoniot compression data are reviewed, and the shock-induced phase transitions and the dynamics are discussed, as well as the EOS of the high-pressure phase up to evem 1 TPa.