Pressure is an important thermodynamic parameter since it allows an increase of matter density by reducing volume. The reduction of volume by applying high pressures leads to an overall decrease of interatomic and intermolecular distances that allows exploring in detail atomic and molecular interactions. Therefore, high‐pressure research has improved our fundamental understanding of these interactions in solids, liquids and gasses. The study of the structure of matter under compression is a rapid developing field that is receiving increasing attention especially due to continuous experimental and theoretical developments. In this article, we give a brief description of the experimental and theoretical methods employed in the study of solid matter at high pressures and summarize the high‐pressure phases of the most relevant elements and inorganic compounds of the AX, A2X, AX2, ABX2, A2X3, ABX3, ABX4 and AB2X4 families giving an overview of the state of the art in high‐pressure research by highlighting recent discoveries, hot spots, controversial questions, and future directions of research. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)