At high pressure, the typical behavior of elements dictated by the periodic table -including oxidation numbers, stoichiometries in compounds, and reactivity, to name but a few -is altered dramatically. As pressure is applied, the energetic ordering of atomic orbitals shifts, allowing core orbitals to become chemically active, atypical electron configurations to occur, and in some cases, non-atom-centered orbitals to form in the interstices of solid structures. Strange stoichiometries, structures, and bonding motifs result. Crystal structure prediction tools, not burdened by preconceived notions about structural chemistry learned at atmospheric pressure, have been applied to great success to explore phase diagrams at high pressure, identifying novel structures in diverse chemical systems. Several of these phases have been subsequently synthesized. Experimentally, access to high-pressure regimes has been bolstered by advances in diamond anvil cell and dynamic compression techniques. The joint efforts of experiment and theory have led to startling successes stories in the realm of high-temperature superconductivity, identifying many novel phases -some of which have been synthesized -whose superconducting transition approaches room temperature.