Proteins, the nano-machines of living systems, are highly dynamic molecules. The timescale of functionally relevant motions spans over a very broad range, from femtoseconds to several seconds. In particular, the pico-to nanoseconds region is characterized by side-chain and backbone anharmonic fluctuations that are responsible for many biological tasks like ligand binding, substrate recognition and enzymatic activity. Neutron scattering on hydrated protein powders reveals two main activations of anharmonic dynamics, characterized by different onset temperature and amplitude. Here we review our work on synthetic polypeptides, native proteins, and single amino acids to identify the physical origin of the two onsets —one involving water-independent local dynamics of methyl groups and, to a minor extent, of aromatic side-chains, and the other one, known as " protein dynamical transition " , concerning large scale functional protein fluctuations, most likely induced by a crossover in the structure and dynamics of hydration water connected with the second critical point hypothesis.