The interpretation of seismic data and computer modeling requires increased accuracy in relevant material properties in order to improve our knowledge of the structure and dynamics of the Earth's deep interior. To obtain such properties, a complementary method to classic shock compression experiments and theoretical calculations is the use of laser-heated diamond cells, which are now producing accurate data on phase diagrams, equations of state, and melting. Data on one of the most important measurements, the melting temperatures of iron at very high pressure, are now converging. Two other issues linking core properties to those of iron are investigated in the diamond cell: One is the melting point depression of iron in the presence of light elements, and the other is the structure of iron at the conditions of the inner core. First measurements on eutectic systems indicate a significant decrease in the melting point depression with increasing pressure, which is in contrast to previous predictions. X-ray diffraction measurements at simultaneously high pressure and high temperature have improved significantly with the installation of high-pressure beam lines at synchrotron facilities, and structural measurements on iron are in progress. Considerable efforts have been made to develop new techniques to heat minerals at the conditions of the deep mantle in the diamond cell and to measure their phase relations reliably. Even measurements of the melting behavior of realistic rock compositions at high pressure, previously considered to be impossible in the diamond cell, have been reported. The extrapolated solidus of the lower mantle intersects the geotherm at the core-mantle boundary, which may explain the seismically observed ultra low velocity zone. The diamond cell has great potential for future development and broad application, as new measurements on high-pressure geochemistry at deep mantle and core conditions have opened a new field of research. There are, however, strict experimental requirements for obtaining reliable data, which are summarized in the present paper. Results from recent measurements of melting temperatures and phase diagrams of lower mantle and core materials at very high pressure are reviewed. ¿ 2000 American Geophysical Union