The study of phase transitions in materials under high pressure and high temperature is a very active research field. In the last few decades, many important discoveries have been made thanks to the development of experimental techniques and computer simulation methods. Many of these achievements affect various research fields ranging from solid-state physics, chemistry, and materials science to geophysics. They not only involve deepening knowledge on solid-solid phase transitions, but also a better understanding of melting under compression. These modern discoveries, as well as the impact of pressure on structural, chemical, and physical properties, are central to the current Special Issue. Amongst other topics, it places particular emphasis on phase transitions and their effects on different physical properties.