Supersolidity of ice, which was proposed in 2013 and intensively verified since then [C. Q. Sun et al., Density, Elasticity, and Stability Anomalies of Water Molecules with Fewer than Four Neighbors, J. Phys. Chem. Lett., 2013, 4, 2565-2570; C. Q. Sun et al., Density and phonon-stiffness anomalies of water and ice in the full temperature range, J. Phys. Chem. Lett., 2013, 4, 3238-3244], refers to the water molecules being polarized by molecular undercoordination, which is associated with the skin of bulk ice, nanobubbles, and nanodroplets (often called confinement), or by the electrostatic field of ions in salt solutions [X. Zhang et al., Mediating relaxation and polarization of hydrogen-bonds in water by NaCl salting and heating, Phys. Chem. Chem. Phys., 2014, 16(45), 24666-24671; C. Q. Sun et al., (H, Li)Br and LiOH solvation bonding dynamics: molecular nonbond interactions and solute extraordinary capabilities, J. Phys. Chem. B, 2018, 122(3), 1228-1238]. From the perspective of hydrogen bond (O:H-O or HB with ":" representing the lone pairs on O2-) cooperative relaxation and polarization, this review features the recent progress and recommends future trends in understanding the bond-electron-phonon correlation in the supersolid phase. Supersolidity is characterized by a shorter and stiffer H-O bond, longer and softer O:H nonbond, deeper O 1s energy band, and longer photoelectron and phonon lifetimes. The supersolid phase is less dense, viscoelastic, and mechanically and thermally more stable. Furthermore, O:H-O bond cooperative relaxation offsets the boundaries of structural phases and increases the melting point while lowering the freezing temperature of ice, which is known as supercooling and superheating.