Diamond-anvil-cell and shock-wave technologies now permit the study of matter under multimegabar pressure (that is, of several hundred GPa). The properties of matter in this pressure regime differ drastically from those known at 1 atm (about 105 Pa). Just how different chemistry is at high pressure and what role chemical intuition for bonding and structure can have in understanding matter at high pressure will be explored in this account. We will discuss in detail an overlapping hierarchy of responses to increased density: a) squeezing out van der Waals space (for molecular crystals); b) increasing coordination; c) decreasing the length of covalent bonds and the size of anions; and d) in an extreme regime, moving electrons off atoms and generating new modes of correlation. Examples of the startling chemistry and physics that emerge under such extreme conditions will alternate in this account with qualitative chemical ideas about the bonding involved.