Recent high-pressure experimental and theoretical studies provide growing evidence for fundamental changes in bonding properties of many materials under deep Earth conditions. The crystal chemistry of materials at high pressure, especially those containing open-shell elements such as Fe, can differ markedly from that at low pressure and in low-pressure phases. On the other hand, concepts such as transferable ionic radii and coordination polyhedra, which are useful for describing structure and bonding in low-pressure phases, can be successfully applied to some systems (e.g. those containing closed shell ions) if effects of ion compression and orbital hybridization are taken into account. Recent results for simple oxides, silica, perovskites and metals to mantle and core pressures and temperatures are briefly examined.