We describe the application of the molecular dynamics (MD) method to simulate structures and physical properies, including volume compressibilities, volume thermal expansivities, enthalpies, and atomic thermal vibrations, for the MgSiO3 polymorphs and iron. The MD simulation is shown to be very useful and powerful for predecting properties especially under conditions unavailable in the laboratory, such as extremes of temperatures and pressures prevailing in the Earth's deep-interior. We use the MD technique to investigate the possibility of high-pressure or high-temperature phase transitions in MgSiO3 and Fe, which might occur in the deep Earth.