This review article describes our neutron scattering experiments made in the past four years for the understanding of the single-particle (hydrogen atom) dynamics of a protein and its hydration water and the strong coupling between them. We found that the key to this strong coupling is the existence of a fragile-to-strong dynamic crossover (FSC) phenomenon occurring at around TL = 225±5 K in the hydration water. On lowering of the temperature toward FSC, the structure of hydration water makes a transition from predominantly the high density form (HDL), a more fluid state, to predominantly the low density form (LDL), a less fluid state, derived from the existence of a liquid–liquid critical point at an elevated pressure. We show experimentally that this sudden switch in the mobility of hydration water on Lysozyme, B-DNA and RNA triggers the dynamic transition, at a temperature TD = 220 K, for these biopolymers. In the glassy state, below TD, the biopolymers lose their vital conformational flexibility resulting in a substantial diminishing of their biological functions. We also performed molecular dynamics (MD) simulations on a realistic model of hydrated lysozyme powder, which confirms the existence of the FSC and the hydration level dependence of the FSC temperature. Furthermore, we show a striking feature in the short time relaxation (β-relaxation) of protein dynamics, which is the logarithmic decay spanning 3 decades (from ps to ns). The long time α-relaxation shows instead a diffusive behavior, which supports the liquid-like motions of protein constituents. We then discuss our recent high-resolution X-ray inelastic scattering studies of globular proteins, Lysozyme and Bovine Serum Albumin. We were able to measure the dispersion relations of collective, intra-protein phonon-like excitations in these proteins for the first time. We found that the phonon energies show a marked softening and at the same time their population increases substantially in a certain wave vector range when temperature crosses over the TD. Thus the increase of biological activities above TD has positive correlation with activation of slower and large amplitude collective motions of a protein.