Pressure has long been recognized as a fundamental thermodynamic variable but its application 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 century have opened a vast new window of opportunities. With the addition of the pressure dimension, we are facing a 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 creates novel materials. This review describes the principles and methodology used to reach ultrahigh static pressure; the in situ probes, the physical phenomena to be investigated, the longpursued goals, the surprising discoveries, and the vast potential opportunities. Exciting examples include the quest for metallic hydrogen, the record-breaking superconducting temperature of 203 K in HnS, the complication of "free electron gas" alkali metals, the magnetic collapse in 3d transition elements, the pressure-induced topological superconductors, the novel stoichiometry in simple compounds, the interaction of nanoscience, the accomplishment of 750 GPa pressure, etc. These highlights are the integral results of technological achievements, specific measurements, and theoretical advancement; therefore, the same highlights will appear in different sections corresponding to these different aspects. Overall, this review demonstrates that highpressure research is a new dimension in condensed-matter physics. III. Multiple Probes for High P-T In Situ Characterizations A. High-P optical absorptive and reflective microscopy and spectroscopy B. High-P inelastic optical scattering 1. High-P optical Raman spectroscopy 2. High-P Brillouin spectroscopy B. P-induced amorphization and its size dependence C. P-induced devitrification D. P-induced polyamorphism and liquid-liquid transition V. "Simple" 1s Electron Systems Under Compression A. The quest for metallic hydrogen B. The rich high P-T phase diagram of hydrogen C. Helium-the widest-gap insulator VI. P-Effects on Electron Bonding Structures A. P-effects on s, p-electron bonding B. Compressional behavior of free electron gas C. P-induced Fermi surface nesting VII. High-P Studies on d-Electron Systems A. Spin-pairing transition B. Mott insulator to metal transition C. Magnetic ordering transition D. Spin-liquid transition E. Phase separation and colossal magnetoresistence in manganites VIII. High-P Studies on f-Electron Systems A. Volume collapse and mixed valences in f-electron materials B. Quantum criticality and quantum phase transition C. f-electron Superconduct...