**Acknowledgements**

I am grateful to William Bassett, Thomas Duffy and Taku Tsuchiya for their contributions to the sections on diamond anvil cells, shock waves and theoretical mineral physics, respectively. I appreciate the courtesy of many colleagues in providing figures to illustrate this paper: Ed Garnero, Quentin Williams, Guoyin Shen, Shun Karato, Nick Schmerr and Stas Sinogeikin; all colleagues have granted explicit permission to use their figures in this chapter, none of which have been published. Portions of this chapter have been adapted and modified from the author's previous publications [3, 7, 8]**.**
