In this review we discuss the relaxation dynamics of glassy and deeply supercooled water in different types of systems. We compare the dynamics of such interfacial water in ordinary aqueous solutions, hard confinements and biological soft materials. In all these types of systems the dielectric relaxation time of the main water process exhibits a dynamic crossover from a high-temperature non-Arrhenius temperature dependence to a low-temperature Arrhenius behavior. Moreover, at large enough water content the low-temperature process is universal and exhibits the same temperature behavior in all types of systems. However, the physical nature of the dynamic crossover is somewhat different for the different types of systems. In ordinary aqueous solutions it is not even a proper dynamic crossover, since the water relaxation decouples from the cooperative α-relaxation of the solution slightly above the glass transition in the same way as all secondary (β) relaxations of glass-forming materials. In hard confinements, the physical origin of the dynamic crossover is not fully clear, but it seems to occur when the cooperative main relaxation of water at high temperatures reaches a temperature where the volume required for its cooperative motion exceeds the size of the geometrically-confined water cluster. Due to this confinement effect the α-like main relaxation of the confined water seems to transform to a more local β-relaxation with decreasing temperature. Since this low-temperature β-relaxation is universal for all systems at high water content it is possible that it can be considered as an intrinsic β-relaxation of supercooled water, including supercooled bulk water. This possibility, together with other findings for deeply supercooled interfacial water, suggests that the most accepted relaxation scenarios for supercooled bulk water have to be altered.