Theoretical methods are indispensible for the study of matter at high
pressure. In the last decade the development of accurate intermolecula
r potentials and the methodologies in classical molecular dynamics (MD
) simulations have greatly facililated the applications of these metho
ds to the study of structural phase transformamtions of solids at high
pressures. More recently, it has been possible to incorporate quantum
mechanical effects into MD calculations. This method eliminates a gre
at deal of empiricism. These first principles calculations have not on
ly reproduced the experimental results for phase transformations but a
lso provided detailed mechanisms and in some cases predicted new struc
tures that may be found at high pressures. The success of MD calculati
ons is illustrated through a review of our studies of pressure-induced
amorphization and phase transitions in SiO2 and TiO2, and the structu
ral memory effect in several materials. Current applications using qua
ntum molecular dynamics on ice are discussed.