Pressure has long been recognized as a fundamental thermodynamic variable but was previously limited by the available pressure vessels and probes. The development of megabar diamond-anvil cells and a battery of associated in-laboratory and synchrotron techniques at the turn of the millennium have opened a vast new window. With the addition of the pressure dimension, we are facing a brave new world with an order of magnitude more materials to be discovered than all that have been explored at ambient pressure. Pressure drastically and categorically alters all elastic, electronic, magnetic, structural and chemical properties, and pushes materials across conventional barriers between insulators and superconductors, amorphous and crystalline solids, ionic and covalent compounds, vigorously reactive and inert chemicals, etc. In the process, it reveals surprising high-pressure physics and chemistry and create novel materials. Exciting examples of pressure-induced phenomena include intermetallic compound-alloy transitions due to 4f electron delocalization, magnetic collapse in 3d transition elements, complication of “simple electron gas” metals, and synthesis of superhard amorphous carbon allotrope. They illustrate the high-pressure research as a new dimension in basic science as well as materials applications. In nature, high pressures are generated inside the Earth and celestial bodies; their interior processes, dynamics and formation are dictated by pressures. Investigations with new-generation high-pressure probes are still at the reconnaissance stage, but they have already shown profound impact on our understanding the geochemistry of the deep mantle, the geodynamics at the core-mantle boundary, the whole Earth water cycle, and the physics and chemistry of planetary ices and gases.