Current interest of high-pressure earth scientists is shifting from upper mantle to lower mantle, from mantle to core, from quenching experiments to high-pressure, high-temperature in-situ measurements, and from static phase equilibrium to large scale dynamical motion. In this paper, frontier report is given on several topics. A precise version of the olivine-modified spinel-spinel-post spinel transformation diagram in the system Mg
2SiO
4Fe
2SiO
4 and of the pyroxene-garnet-ilmenite-perovskite transformation diagram in the system Mg
4Si
4O
12-Mg
3Al
2Si
3O
12 is presented. The 670km seismic discontinuity is well-explained by the dissociation of (Mg, Fe)
2SiO
4 spinel to (Mg, Fe) SiO
3 perovskite and (Mg, Fe) O magnesiowüstite in pyrolitic mantle. Based on the phase diagram, the temperature at the depth of 655km is estimated about 1600°C. Effect of the olivine-modified spinel-spinel-post spinel transformations on the dynamics of the descending slab (plate) is discussed in relevance to the deep focus earthquakes. Recent progress of high-pressure, high-temperature research in the system Fe-H, Fe-FeO and Fe-SiO
2 is outlined with reference to the core formation process in the proto-earth and the composition of the present earth's core. Solubility of hydrogen, oxygen and silicon into molten iron increases remarkably at very high pressure up to 24 GPa. Oxygen and hydrogen might be the chief light elements in the earth's outer core. The silicon content in the core depends on the depth of the magma ocean of the proto-earth.
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