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 T_c 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.