Water is one of the most common substances in the universe and is found in many different phases. At extremely high temperature and pressure, water ice forms a superionic phase (SI) in which the water molecules dissociate into ions, with the oxygen ions forming a crystal lattice structure and the hydrogen ions flowing through the lattice like a liquid. In this thesis, we present a first-principle study of the high pressure superionic ice phase. We systematically explore the superionic phase diagram and carefully study its physical and chemical properties. As a result of this investigation, we find that superionic ice exists in three different phases differentiating from each other in the structure of the oxygen sublattice. One phase is the BCC-SI phase, which has BCC oxygen sublattice and has been predicted by several groups. We find the BCC-SI phase is stable up to about 250GPa. At higher pressure, BCC-SI transforms via a first order transition to the CP-SI phase. The oxygens form close-packed structures in this phase. CP-SI has also been predicted by other authors, though our predicted transition pressure is significantly higher. Finally, we find a third SI phase, P21/c-SI, which would exist at even higher pressure and it is predicted here for the first time. In addition, we use the imaginary-time path integral technique to study the nuclear quantum effects (NQE). We find the NQE changes the SI ice phase boundaries significantly. Compared to the classical results, NQE makes CP-SI phase more stable and increases the transition pressure from about 1.5TPa to about 1.7TPa. We show that the NQE on the SI phase boundary can be explained by thermodynamic perturbation theory to the lowest order. Lastly, we studied the chemical bonding and the electronic structures of high pressure superionic phases. We computed the distribution of maximally localized Wannier functions centers and showed evidence that the chemical bonding in high pressure ice phases is dominated by ionic interactions. This is very different from the low pressure phases, where the water molecules are intact and the intermolecular interactions are dominated by hydrogen bonds.