In this paper, both the dynamics of a protein and its hydration water are investigated by quasi-elastic neutron scattering (QENS) experiments. In addition, molecular dynamics (MD) simulations of a realistic hydrated protein powder model are also introduced to reproduce the experimental results. We start from the introduction of the incoherent neutron scattering method for studying dynamics of a protein and its hydration water. Then we discuss in details the coupling of the dynamics of a protein and its hydration water, including the following topics: the elastic scan and the reduction from it the mean squared displacement (MSD) of hydrogen atoms in protein and its hydration water; evidence of the dynamic crossover from pressure dependence of the measured relaxation time of hydration water in biopolymers by QENS; synchronization of the dynamic crossover phenomena in other biopolymers and their hydration water; an alternative method for detecting the dynamic crossover temperature. We also show our observation of a logarithmic-like beta-relaxation in the study of intermediate time protein dynamics at the end of this paper.