Studies in superconductivity at extreme pressures

High pressure studies have played an important role in the field of superconductivity since the first experiments by Sizoo and Onnes in Leiden in 1925. A rapid dependence of the transition temperature on pressure signals that the material is capable of higher values of Tc at ambient pressure. Significant extensions of the pressure range, most recently to pressures above 1 Mbar using the diamond-anvil cell, have resulted in the discovery of many new superconductors. The transition temperature of Y metal has very recently been pushed by 1.15 Mbar pressure to 20 K, a value for an elemental superconductor second only to that of Ca at Mbar pressures. Such enormous pressures are even sufficient to destroy the free-electron character of the conduction electrons in the alkali metals. Selected experiments are discussed which illustrate these features.