The use of molecular dynamics simulation to investigate the properties of hydration water around proteins is outlined. A variety of structural and dynamical properties of the protein hydration water are reviewed and compared with those of bulk and with the corresponding experimental results. In particular, the accessibility to the protein medium, the hydrogen bond networking capability, the residence times, the diffusive mobility, the relaxation behavior, and the inelastic vibrational features of hydration water are analyzed in framework of the peculiar interactions of water at the protein surface. All these features, which can be traced back to the complexity of the overall protein-solvent energy landscape, are discussed in connection with the role played by hydration water in the biological functionality.