In a recent quasi-elastic neutron scattering experiment on water confined in a Portland cement paste, we find that this 3D confined water shows a dynamic crossover phenomenon at T_L = 227 ± 5 K. The DSC heat-flow scan upon cooling and an independent measurement of specific heat at constant pressure of confined water in silica gel show a prominent peak at the same temperature. We show in this paper that this type of behavior is common to many other glassy liquids, which also show the crossover temperature in coincidence with the temperature of a small specific heat peak. We also demonstrate with MD simulations that the dynamic crossover phenomenon in confined water is an intrinsic property of bulk water, and is not due to the confinement effect. Recently, an extended version of the mode coupling theory (MCT) including the hopping effect was developed. This theory shows that, instead of a structural arrest transition at T_C predicted by the idealized MCT, a fragile-to-strong dynamic crossover phenomenon takes place instead at T_C, confirming both the experimental and the numerical results. The coherent and incoherent α relaxation times can be scaled with the calculated viscosity, showing the same crossover phenomenon. We thus demonstrated with experiments, simulations and theory that a genuine change of dynamical behavior of both water and many glassy liquids happens at the crossover temperature T_L, which is 10–30% higher than the calorimetric glass transition temperature T_g.