The properties of water in biological systems have been studied for well over a century by a wide range of physical techniques, but progress has been slow and erratic. Protein hydration--the perturbation of water structure and dynamics by the protein surface--has been a particularly rich source of controversy and confusion. Our aim here is to critically examine central concepts in the description of protein hydration, and to assess the experimental basis for the current view of protein hydration, with the focus on dynamic aspects. Recent oxygen-17 magnetic relaxation dispersion (MRD) experiments have shown that the vast majority of water molecules in the protein hydration layer suffer a mere twofold dynamic retardation compared with bulk water. The high mobility of hydration water ensures that all thermally activated processes at the protein-water interface, such as binding, recognition and catalysis, can proceed at high rates. The MRD-derived picture of a highly mobile hydration layer is consistent with recent molecular dynamics simulations, but is incompatible with results deduced from intermolecular nuclear Overhauser effect spectroscopy, dielectric relaxation and fluorescence spectroscopy. It is also inconsistent with the common view of hydration effects on protein hydrodynamics. Here, we show how these discrepancies can be resolved.