Although solids are not very compressible, extreme pressure will still compress solids to a measurable degree.

Some solids will also undergo phase changes when subjected to increasing pressure - from one solid structure to another. As previously noted, ice may actually melt if pressure is applied near the melting point temperature of the ice (a solid to liquid phase change vice a solid/solid phase change). A good example that most people are familiar with is the formation of diamonds. The tetrahedral crystaline structure of diamonds is actually not thermodynamically stable at atmospheric conditions, but from a kinetic standpoint the conversion back to graphite or other stable solid structure is so slow that it might as well be stable. To get it to convert to the diamond structure requires very high pressure.