The unusual properties of water, including the thermodynamic anomalies of the liquid, the existence of more than one amorphous ice form, and the abnormal mobilities of the water ions, derive from the tetrahedral network of hydrogen bonds that hold the molecules together. Under applied pressure the topology of the network changes but local tetrahedrality is preserved as the system explores a variety of different phases until at extreme pressure the molecules dissociate into ions and the hydrogen bonds collapse. Modern ab-initio simulations provide a unifying picture of these processes. In this talk, I will review recent progress in these studies stressing connections between theory, simulation, and experiment.